I was playing a friendly match tonight and had a disagreement with how asteroids work.
My opponent landed Horton on a rock. He rolled no damage, lost his action and his shot, which we both agree is the correct reading of the rules.
The following turn, to get off the rock the movement template had to again touch the rock. It was my understanding that this means he again has to roll damage and lose his action. He said that he'd already resolved that asteroid overlap last turn.
I can't seem to find a disambiguation in the rules, which is why I think I'm right. Each turn you just follow the rules as printed, nothing carries over as far as previous collisions.