Things will grind to a halt.
What would a Bitcoin be worth then? Nothing, you could have guessed it yourself. Meanwhile, the earth kept spinning with a lot of people living in the real world wanting things now instead of never as thought out by a very clever but unpractical scientist. Perhaps in a study room people have no immediate wants and will postpone their purchases until they die, but real life works just the other way around.
Massive deflation is quite a ride (as is hyperinflation) but mild deflation is nothing to worry about. Nobody will postpone a purchase because it will be 1% cheaper next year while more than 1% of your expected years of life is gone by then. Of course, deflation is a big problem if you permitted a bubble to build up which market forces try to wipe out exactly by deflation. But deflation is not the problem then, but the solution of free market forces. The real problem is blowing that bubble in the first place. Economist who keep ignoring this, drive me crazy.
Bitcoin would not stop the economy from going on. Things will magically stabilise between consumption and savings, depending on everchanging preferences. The price of money will adapt, solving fluctuations in that balance. That's the way free markets are supposed to operate. Don't let the argument of deflation scare you from thinking about it more thoroughly.