It could be faulty equipment, faulty wiring or a faulty breaker.
Temporairily disconnecting the smoke detectors can eliminate them as a cause.
Swapping circuit breaker connections can rule that out.
If you have an arc-fault circuit breaker, a loose connection can cause a trip. I'd check for a tight connection in the breaker panel (hot and neutral).
Loose connections and intermittant short circuits can also be checked for at junction boxes on the citcuit, looking for any evidence of arcing. I'd start at the first junction box on the circuit and work towards the last.

Is this a GFI breaker? I've seen similar behavior with overly touchy GFIs.

Thanks! It is indeed an ARC FAULT (Eaton, Type BRAF).

I can't get it to turn on, I should try again, turning it off completely first, and then turning it on.

I thought I did that, now if it does not come on, does that mean that it needs to be replaced (of course, I still have the original cause to figure it out).

It is simply a bad acr-fault. Extremely common from that time frame.
The breakers from that time are NOTORIOUS for nuisance tripping.

I'm not familiar with the EATON BR line but I can tell you that the earlier GE AFCI's were terrible on nuiscance tripping. I replaced my MOD2 ones with MOD3 (the one with the rocker to test both series and parallel faults) and I've not had a nuisance trip since.

It may also be that you have a neutral-to-ground fault, which will trip an AFCI. If there is, it's probably in an outlet box. Pull the outlets on the circuit and see if you find a ground wire touching the neutral screw of the outlet, or some such.

You might see if the current type BR arc faults are newer than the one installed. I had tons of nuisance trips with the GE mod2 arc faults that went away when I replaced them with the mod3.