Capacitors are prime failure points, other than that the thing should last for decades. LEDs will eventually burn out, as will voltage regulating/dumping resistors, springs in the keyboard will weaken, sooner or later the floppy drive will fail, but they are generally very robust. Please correct me if I'm wrong on this point - the custom chips in an A500 are NOT eprom or such, they are "genuine" silicon and can be expected to survive until punished by truly excessive quantities of radiation (nuclear strike nearby) or a random cosmic ray from a stellar event just happens to punch a hole clean through the substrate...
It also makes no real difference whether you use it or not, however powering up/down is the major cause of stresses to the system (thermal shock), so there is little to be gained from trying it out now and again "just to check it's still ok" as that is when there is the greatest likelihood of damage/failure.
I don't know the MTBF of an entire A500 though...