This camera is a hand-me-down from my dad which I previously thought was broken until I put a battery from my AT-1 in and it fired just fine (turns out 3 or 4 LR44's I tried in 2017 were all junk).
However, despite it cocking fine it seems to have problem with the cocking arm not catching the whole time. When you cock the shutter it only moves the shutter, advances the film, cocks the mechanism, etc. at the very end of the travel of the cocking lever. So I need to pump it from 3/4 of the way to the full end of travel in order for the shutter and cocking lever to be reset and then it's ready to fire.
I've yet to put film into it because I'm not sure if I want to waste a roll on this if cocking it 360+ times will harm the camera.
Is this a common problem with the AE1? It's hard to research because (like was also the problem for me a few years back) the cocking arm being stuck and won't go beyond the first quarter of travel seems to be all what comes up when you look up AE-1 cocking arm problems. Hopefully it's something cleaning and lubricating can fix without needing to disassemble the cocking arm mechanism and linkages.