This is kind of a long answer to your questions.
I agree with Pierre, above, that this is an unusual circumstance. Your details are helpful. Thanks.
One circuit also feeds smoke detectors and another has a closet light. The other two are strictly outlet circuits.
OK. Four AFCI circuits. Two that are
receptacle outlets only, one that is for a closet light only, and one that is for smoke detectors only . . . right?
I gather from this that there are no overhead or wall luminaires. (If there are luminaires, paddlefans, etc., do they have compact fluorescents, or are they LEDs, plain old incandescent, electronic or magnetic ballasted fluorescent, electronic or magnetic transformer supplied low voltage, or what?)
As we worked finishing the house sometimes when we got there the AFCI's were tripped and other times they were not. Sometimes we were gone for several days and they would be ok and other times they were tripped when we got there. We never left anything plugged in when we left.
This is the really curious set of symptoms. Curt, above, asked about the AFCI manufacturer's name.
My son moved in about four months ago. The AFCI's are still doing the same thing. He noticed when they trip it is not simultaneously but they all go within 2-3 seconds. It's like - one trip - two trip - three trip - four trip.
Again, this is really curious.
Are each of the circuits, on the load side of the AFCI breaker wired with a hot and neutral that are not in contact with any other circuit conductors?
If the wiring method you chose is NMB cable, is the bare copper carefully installed at each and every box so that it is not possible for it to touch the neutral (white)?