All was well for a year and a half, then the GFCI breaker started tripping for no apparent reason. I assumed that the breaker had gone bad, so I replaced it. The new one still trips, albeit after a longer period of time (old, about three minutes; new, three to 20 hours).
I've pulled all the outlets and tightened the screws.
Still the breaker trips after some hours, whether the circuit gets loaded or not.
One thought I've had: the original romex for the longest run of this circuit is from that period of time (1960s?) when the ground wire is smaller gage than the main conductors. Could that be causing the problem?