Skepticism over 'Violations of Nature'
A relatively large bias has existed against the supernatural for a while in modern times. Already in the 17th century Spinoza denied the existence of miracles because they "violated natural law." In the early 1900's, a biblical scholar named Adolf von Harnack delivered a lecture which basically said that in ancient times the laws of nature weren't well understood or respected, and as a result we encounter countless miracle stories. Miracles can't exist because they break the immutable nature of reality.
The Origin of the Anti-Miracle Mentality
Harnack might be correct about the origin of many miracle stories, but he certainly isn't correct about his unconditional adherence to the laws of nature. He spoke around 1909, a time when Einstein's General of Theory of Relativity hadn't even been published (1916) or tested (1919), shaking the world by the rejection of Newtonian physics. It's a characteristic mark of the 19th century, carried over from the physical accomplishments since the days of the Enlightenment, to blindly believe in their progress' inerrant superiority and to question all tradition. Not only was the Bible considered full of forgery, but also the authenticity of various ancient texts, such as Herodotus' Histories, or Tacitus' Annals. Euripides' genius in Tragedy was even eclipsed [Arthur S. Day ed., Euripides Vol. I (Loeb Classical Library: 1916, pp.ix-x)]. The general attitude that prevailed was one of being close to answering all questions about the universe: there was literally a (rather short) list of questions left unanswered until the theory of "everything" was complete.
This carried over into mathematics. In the early 20th century, the great mathematician, David Hilbert, inaugurated a famous quest to have all results in math reduced to a complete set of consistent axioms. This attempt was frustrated by Kurt Gödel in 1931 when his Incompleteness Theorems proved this was impossible. The result was expanded beyond mathematics and more philosophically for logic in 1936 by Alfred Tarski with his Undefinability Theorem, and that same year Alan Turing did the same for Computer Science and the Halting Problem. With so many negative results, it almost seems like math, science, and logic were crashing down, especially compared with the previous century's confidence and optimism. If only skeptics of religion would see that errors in the conclusions of a philosopher do not necessarily imply mistakes in the philosophy: not only were many ingenious men mistaken in math and science, but it almost seemed like the subjects themselves had holes.
At any rate, the point is that Harnack lived at a time when these facts about the erroneous nature of his and others' dogmatic view of reality and the universe were still in the future. Even if we take a naturalistic view, we know from Quantum Mechanics that classical physics breaks down at the subatomic level, and in places such as at the singularity of a black hole. And the laws of nature weren't always the way they are now - they were formed and stabilized some time in the finite past after the Big Bang.
Where are all the Miracles?
Not that the liberal sciences are without their own merit - the Catholic Church would've never sponsored universities if it weren't the case. But when one starts making assumptions about areas one is blind in, that's where a scientific observation becomes a philosophical leap.
But we're still left with the question, "Why don't we see documented, indisputable miracles today?" After all, we have video cameras and plenty of other modern technology. The implication is that with the secularization and education of a very large number of the population, which vastly exceeds that of previous centuries, the "superstition of the supernatural" has proportionately disappeared.
Yet, even if we ignore a large amount of literature that includes personal testimony to the contrary, this is quite a dangerous statistical assumption. I'm not going to argue something like, "there could always be that one miracle nobody but a few people could've seen," or, "the miracles are now purposefully hidden," and try to avoid the issue due to gaps in our ever-growing knowledge.
Here's a very real and well-documented, naturalistic (!) parallel. In the recent past, such as the 19th century, when modern technological conveniences such as calculators and computers didn't exist, there were quite a few mathematical prodigies who could calculated huge numbers at an instant.
C. Stanley Ogilvy and John T. Anderson note several of these people, in some cases children at the age of 9 such as Zerah Colburn and Zacharias Dase (pp.103-6). This is what they observe and conclude about present-day prodigies:
Nearly all of the older books about numbers or mathematical recreations contain accounts of calculating prodigies. The arithmetical wizard was a subject of wonder and admiration to the nineteenth- and early twentieth-century reader. Today there seems to be less general interest in the human calculator, perhaps because his feats have been so far surpassed by his mechanical counterpart. When a Colburn or a Dase multiplied two large numbers together in one-twentieth of the time it would take to do the arithmetic by longhand, people were impressed partly because there was no other way to get the answer. But now, when a machine can do the same "problem" in a twenty-thousandth of the time, with virtually no chance of error, the human performance, while just as noteworthy as it always was, fails to make the same impression. It happens that there have been no famous calculating boys born in the twentieth century. When the next one turns up, it is a safe bet that his appearance will cause little stir. [Ogilvy and Anderson. Excursions in Number Theory (1988), pp.106-7; underline emphasis mine].
So here we have a very good, secular example of technology eclipsing the astounding. Let's take one of the more locally common miracles in the Bible. For example, in 2 Kings 6:1-7, Elisha and his guild of prophets go to the river Jordan to make a bigger house for themselves. One man's axehead falls into the water and Elisha makes the iron float so he can recover it. Nowadays, someone can easily do the same with a big magnet. They had magnets back then too, probably, but not big ones that could've been used efficiently, or at all. Imagine if someone came along with a giant magnet or some kind of magnetic sonar - Elisha would've never performed any miracle, small-scale or not.
Of course, there are many areas where our technology isn't sophisticated enough to overshadow a miracle, though this is a separate issue. As a result of the infrequent and unpredictable nature of miracles, man naturally resorts to helping himself on a consistent basis by technology. This difference in knowledge and advances between antiquity and today led many skeptical attitudes toward Christianity to give rationalistic explanations once a universal system of laws was suspected starting with the Renaissance. For example, Jesus' miracles were naturally explainable and he was a skilled magician (in the non-religious sense). That deceivers have always existed and didn't need technology is perfectly illustrated by Lucian of Samosata's Alexander of Abutoneichos, for example. But without a doubt we also have a reflection of an attitude due to a phenomenon like the one given by Ogilvy and Anderson.
Not only does this bias make it difficult to observe what little could've been credibly observed and reliably reported of miracles, but miracles were always few and far in between. There are literally like three miracles in the entire Bible that were seen by the vast majority of a number of people, so that they could be recorded, especially with the ancient rate of illiteracy. These three are: (1) the Exodus, (2) Joshua's Long Day, (3) the Resurrection. This isn't an excuse for the absence of miracles. Most of what we know about various cultures comes from archaeology and not written sources, especially when it's a small, isolated culture as in the case of Joshua's Long Day and the Resurrection.
The Exodus is probably the best case for a miracle that could've been reliably recorded (by the Egyptians, since the Hebrews were basically at that point semi-nomads). However, the Egyptians weren't in the habit of recording losses; no ancient (or modern) race really was. For example, the Battle of Kadesh between Egypt and the Hittites resulted in a stalemate. The Egyptians claimed it was an overwhelming victory for them and so did the Hittites. Not only that, but the plagues and splitting of the Red Sea are themselves, while brutal, not too miraculous of a phenomenon. The Bible says the Red Sea was split by a strong wind from the East (Exodus 14:21). Napoleon encountered a similar phenomenon during his Egyptian campaign at the Suez (Christian Hauer and Ernest Young, An Introduction to the Bible (7th ed), p.96). Raining frogs? There are many cases of raining frogs, fish, or snakes in modern times. Blood-red Nile? Chemical processes can give that effect and it's not necessarily supernatural or crazy enough to deserve a record. Dead animals, etc, result from the poisoned (blood-red) Nile. All of the plagues combined are certainly noteworthy enough, but once again, who wants to preserve their misfortunes for all memory in posterity. Moreover, only a fraction of history has been recorded, and only a fraction of that has reached us. The eruption of Thera in the 17/16th century BC caused some pretty intense natural disasters for the Egyptians as well, and the only record we have of it is the Tempest Steele.
Joshua's Long Day would have been witnessed by many people. But how many would have recorded it, and how would that record have been interpreted? The various cultures who have a long day (or long morning - Chinese and Kiwi myths), could be interpreted as legendary, and basically would've been as reliable as a myth. A naturalistic explanation could easily come to mind, just like the first century Roman historian, Thallus, attributed the darkness at Jesus' crucifixion to a solar eclipse, despite the fact that this is impossible during Passover, which is why Julius Africanus and Eusebius (who quotes him), reject the idea.
The Resurrection is the best known miracle of the Christian Bible. Without it, Christianity's central impact is gone. Yet not only were rationalistic explanations ready to be given, there wasn't much of a chance anything would've been recorded anyway. The Jewish leaders who condemned Jesus claimed his body was stolen by his disciples (much like John the Baptist's - Mark 6:29). Jesus' appearance was mostly to believers. Even hundreds (1 Cor. 15:6) wouldn't really have any way of reliably recording it or being believed except by other believers anyway.
No one would have been interested in recording the Resurrection. The Romans were interested in their own affairs and already there was a massive anti-Jewish bias amongst many of them. Tacitus, probably vexed by myriads of religiously related insurrectionists which Josephus details, calls it a superstition without any investigation. The Jewish leaders obviously considered Jesus a heretic, demon-possessed, and a deceiver. The Jews of Jerusalem (and abroad), under the influence of these leaders, tried to pin the label of "rebel" (insurrectionist) by claiming he and Christians were preaching a king other than Caesar. The same thing happened to the 12th century philosopher, Peter Abelard - beloved by all of France with countless students coming to hear his lectures from all over Europe. But at the Council of Soissons, some clergy who hated his theological positions incited the Parisian crowd against him as he records in his Historia Calamitatum. Not even Christians had a motivation to write anything down: everything was spread by (reliable) witnesses and word of mouth. Paul's letters don't even mention Bethlehem, Nazareth, or much about Jesus' earthly life. The Gospels don't start to appear until the late 1st century.
Many non-theists ask the popular objection, "Why doesn't God heal amputees?" Restored sight could be natural or psychosomatic (e.g. the temporary blindness of Richard Burton's companion, John Speke on one of their trips in Africa). The same could be said of many illnesses. But a restored limb is something else. Although the healings of the paralyzed and lame/crippled comes close (Mark 2:1-12; John 5:1-17), there's an important observation to be made here: miracles weren't that commonplace in the ancient world either. Superstitions were well-known to be fictitious imagination spread by ignorant people. The Church in the Middle Ages regarded belief in witches as superstition (e.g. the Council of Paderborn in 785). When Jesus heals a blind man since birth, he responds in John 9:32 by saying, "Never since the world began has it been heard that anyone opened the eyes of a man born blind." In Judges 6:12-13 an angel tells Gideon that the Lord is with him, to which Gideon asks, "Please, my lord, if the Lord is with us, why then has all this happened to us? And where are all his wonderful deeds that our fathers recounted to us, saying, ‘Did not the Lord bring us up from Egypt?’ But now the Lord has forsaken us and given us into the hand of Midian.” He's talking about several hundred years in the past: apparently the last miracles he and the people around him had heard of. This goes to show how poor records were as we mentioned, and even then they were merely what we might regard as "old wives' tales" today (whether accurately or not is another question). In Judges 19:30 the people again clearly never saw any wonders on the scale of the Exodus since Moses, and aside from cryptic references to angels (e.g. Judges 2:1), it's unlikely they saw many miracles at all. Most of the communication with God was through prophets or the Urim and Thummim - all naturalistically explainable if one wanted to chalk up the results to chance. Similarly, the priests themselves didn't often hear from God directly: in 1 Samuel 3:1 it's stated that visions from God were rare in those days. All these things happened, of course, as Judges 2:1 and much of the rest of the Bible clearly and consistently says, because of their sins.
The bottom line is, we can always fall for bias, sensibly or not. But while labels can be helpful, sometimes the details need to be investigated further since they can easily mask genuine beauty.