If you have a Zinsco panel in your house get it replaced or keep you fire insurance up. Zinsco=bad junk.
I’ve seen plenty of these breaker panel units pop, usually in shops (plug in too much stuff - i.e. can’t have the coffee maker and the electric heater on the same circuit.
It is not unusual for them to be just slightly off the “full on” position when they pop. I always assumed that was normal. (Some pop to the middle instead) That was enough that a visual inspection may not notice. It’s just a little soft of you push it to “on”. You have to actually click it full off then full on again to reset.
I also replaced a GFCI outlet that would pop regularly, sometimes when nothing was happening on the circuit. OTOH, we were watching TV once when the stereo amp began smoking, and the stove, microwave, two subwoofers, several electronic devices all fried. We now have a whole house surge protector.
So yes, these devices including breakers could become too sensitive and occasionally pop for no reason. As others said - try replacing. If that fails too - time for some serious inspection of what’s on the circuit.
OP could also have the heat from the A/C load heating up the breaker next to it and if that is closer to capacity, it might be enough to push it over the edge.
I’ve looked through the comments and haven’t seen a check of the window AC wiring. Also, the receptacle at the AC end needs to be checked as well (loose wires, burnt insulation, missing insulation, etc…). Not an electrician nor do I play one in a TV series but it’s been my experience that the wiring and receptacles have more problems than the breakers.