The Invisible Hand works as well as it ever did... it was always a thought experiment. Adam Smith postulated that the Invisible Hand would act in a self-regulating market in the presence of three things: perfect information, perfect competition, and perfect mobility.
None of those are possible. However, labeling and fraud regulation bring us closer to perfect information. Anti-trust laws bring us closer to perfect competition. Perfect mobility is harder to accomplish through regulation, but the abolishment of Jim Crow laws, redlining, and other such practices that dictated where people could live and do business helped. More recently, the Internet (developed by the Defense Department and a public university) has done much to bring us closer to perfect mobility.
The Invisible Hand was never thought to prevent market fluctuations, though. In fact, Adam Smith and those who study him acknowledge freely that the efficient free market often *does not* address the needs of people. In a free market, those who can't perform will die. This is where the irrationality studied by behavioral economists comes in... we are social creatures, and so there is some "rational" behavior that gets overridden by our survival instincts. We know that if we always work against each other, we'll die. At first, only the weaker ones, but eventually, we will all die off because we fundamentally need each other.
Where the Invisible Hand seems to be failing, it is actually a failure of the very regulations intended to preserve it. Deregulation destroys a self-regulating market, by moving us further from perfect information (like information about what candidates the company donates money to), perfect competition (next I have to explain to the FCC why they shouldn't let AT&T buy T-Mobile), and perfect mobility (so long as we order on Amazon).