I had a fence climbing bot fall 15 feet onto a concrete surface without any serious damage. The same RCX has survived 7 years of FLL on a team that:
-likes fast robots
-uses the "ram into wall to correct angle" approach to self correcting.
In general, mindstorms components are quite strong. I've only had one out of something like 25 motors burn out, and that was in an experiment to test the strength of the motors that looked kind of like
this The only real problem I've had is with the toutch sensors jamming or becoming unable to detect a push after repeated, strenuous use, such as the wall hitting described above.
In my experience, RCXs acting weird are more than likely IR issues. I have seen robots at FLL competitions do some REALLY weird things due to IR focusing cameras. As others have said, changing batteries or realoading firmware usually solves the problem