In their 1990 book, A Non-Random Walk Down Wall Street, Andrew Lo and Craig MacKinlay document a number of persistent predictable patterns in stock prices. One of these "anomalies" is variously known as lead-lag or serial cross-correlation, and it says that the returns of larger, more liquid stocks tend to lead the returns of less liquid small-capitalization stocks. Lo and MacKinlay showed that the degree of lag is greater than what could be explained by the lower trading frequency of small-cap stocks (nonsynchronous trading). A 2005 working paper by Toth and Kertesz claims to show that the lead-lag effect has "vanished" over the past 20 years. Meanwhile, other anomalies documented at the time, such as long-horizon overreaction (first documented by DeBondt and Thaler (1985)), appears to be alive and well (see McLean (2010)).
Why do some anomalies persist even decades after they are discovered while others have seemingly been arbitraged away to nothingness? What is it about those anomalies that are still around so many years later that prevents them from being arbitraged away? Conversely, what is it about the short-lived anomalies that made them so fragile?
Note: This post was inspired by a a blog post, Of Hurricanes and Economic Equilibrium, although I do not agree with the author's conclusions.
Bounty update: As promised, I created a new bounty for RYogi's answer, which is "exemplary and worthy of an additional bounty". It will be awarded shortly, as the system requires some lag time until the bounty is awarded. Feel free to add your own up-votes to his answer in the mean time.