We've seen lately a lot of ingenious attacks against previously hardened crypto. My guess is that the algo we use for key signing will eventually fall. While we could always switch, the fact that the algo fell would undermine confidence in the currency and render it worthless.
Crypto experts claim that these algorithms, like SHA256, don't just fail all of a sudden. They first show the signs of weaknesses as mathematicians find a new ways of attacking them. There is always big time gap between showing the weakness and first demonstrated practical exploit, and those exploits usually are applicable in special cases. I don't see why would change from SHA256 in, say, 10 years from now, with some much, much more secure algo undermine the confidence in the BTC. It would be natural evolution, and even if then would be SHS256 realistically exploitable, accumulated proof of work would be barrier to any attack. And the story will probably repeat in few decades after that, and so on.