Real-world currencies have backing. The ability of dollars to hyperinflate or hyperdeflate is bounded by the fact they can be used to pay debts to the United States Government that are denominated in dollars. Their value recursively emanates out from there, but that's the base case. That's also why the fall of the US government would be pretty much immediately followed by the fall of dollars, as has happened to other government-backed currencies. Stripped of its backing, currencies completely collapse in practice. The recursive base case is gone and if the currency briefly holds on it's a Wile E Coyote off the cliff moment, and in the modern connected world I can't imagine it would be more than a few
minutes.
At some point, BitCoin faces some dip in currency confidence. Not because it's "BitCoin", but because all currency face periodic confidence crises. All the major world currencies have faced them in the past three years. But they didn't simply collapse because they have backing. I don't know what stops the first BitCoin currency crisis from completely collapsing the currency, because when BitCoin holders ask themselves, "Hey, what is this really good for?", I don't have an answer. I know what a dollar is good for: Not being put in jail by the United States Government due to unpaid debt. Ultimately, without trying to be too philosophical, dollars are backed with men with guns (and the privilege of them not being pointed at you).
Contrary to apparently popular belief, currencies aren't merely arbitrarily-agreed-upon numbers that we all trade with. Every currency I know has some actual backing. Even the fancy electronic ones we've seen spontaneously develop online, they all have some form of local economy-appropriate backing. It isn't always "gold" (literal or electronic), but so far the "men with guns" approach has proved successful in the real world. BitCoin is an apparently-good design for the arbitrary number approach, but until it solves the backing problem I won't be putting one dime into it. As much as I don't particularly enjoy having the US government as my currency backing I do not see how going to a backing-free currency is the solution.
The currency can still hyperinflate even if it is physically impossible to produce more by virtue of people raising all BitCoin prices as their confidence in the currency collapses. But instead of hyperinflation producing lots more BitCoins, then collapsing the economy, hyperinflation will simply directly collapse the economy as it takes ever increasing amounts of the BitCoins in the world to buy a service, until eventually even every BitCoin in the world isn't adequate. Hyperinflation is a symptom of lack of confidence in a currency, not a cause. (Of course observing hyperinflation can further decrease confidence, but the hyperinflation started in the first place because of lack of confidence.)
BitCoin advocates tend to get very angry when I point this out. I think it's because they have no answer to this. The site used to have a FAQ that addressed this, but it just sort of mumbled words and now it's gone because it was actually better just to ignore the problem. My challenge would be to anyone who claims that currencies are somehow backing-free is show me the successful currency of any kind that really is just an arbitrary number with no backing that has reached any sort of significant size, shall we say, a million dollars or so worth of an economy? (All the electronic currencies like Microsoft Points are well above that size, for instance.) And I'll show the backing. It isn't always a physical item, especially in the electronic world, but it's always something that serves as a locally-appropriate backing.
("So why's it worth so much now?" It's in a bubble generated by all this publicity. What happens the first time this bubble even threatens to pop? That's when you'll really find out who is right, me or them. Oh, and I'd predict an even larger burst of publicity and public braggadocio if it looks like that's going to happen; that will be the only way to forestall the inevitable another few days.)