The stereo in a 1991 Toyota Celica will power off when you drive over a bump or pothole and won't come on again for minutes to hours what can be done?

I suspect that you have a loose power wire...hopefully it is right behind the radio and all you got to do is resecure it well. That could explain why when you hit a pothole it turns off and then touches just enough to turn on later from the movements and then turn off again. So remove the radio and just secure everything and see how it goes...or it could be dirty/coroided so look for that.