Bimetallic strips can fatigue, tho it's rarely the cause of a breaker failure. A 50 year old breaker may have never tripped and only been operated a handful of times over its lifespan. Corrosion, heat, stiction (static friction), mechanical jams, etc. can all cause a breaker to fail.
Some breakers, like the old 2p FPE Stab-Lok, are prone to jamming once they trip. In cases like those, I'd replace a tripped one like a fuse (treat it as a one-time OCPD). Other breakers, unless there is visible damage to the case, handle, rivets, lugs or stabs/bolt on to the buss, it is opening well before its rating, will not stay on, or feels 'weak' when operating, I wouldnt replace a tripped breaker. Since they dont come with a counter, there is no way to know if it has tripped once or five hundred times.
GFCI and AFCI breakers ofc should be replaced if they will not trip with the button, or reset correctly.
In our other house, 5 of the 6 original thermostats for the baseboard heat installed in 1969 are still operating, and within a degree or two of the setpoint vs actual air temperature. Overloads in can lights are also bimetallic strips, and the contact to the bottom of the bulb is likely to fail before they do.