Apparently some European-made air-to-air missiles are subject to a limit of how many “captive” flights they can tolerate - i.e., being carried on the pylons or wingtips of a fighter aircraft, in flight - since each such flight subjects the missile to a considerable amount of physical stress and vibration. I want to ask if this is true of pretty much all aircraft-carried weapons in general, and the American ones as well (AMRAAM, Sidewinder, etc.)?
It’s hours not flight but yes. They have both shelf life (time they can be stored) and air life, the amount of hours they can fly.
IIRC, AMRAAM is 1500 hours.
In reality since other components like the rocket motor and the missile battery also need periodic maintenance separately from the above, the missiles will have a shorter time in between refit that the hours/years.
A German Company has begun a Programme by which they modify old Sidewinders at the end of their life to become air to ground missiles.
Gotta love upcycling 
OK thanks - wait, so if there is refitting, the AMRAAM can last longer than 1,500 hours? Or shorter?