At first I thought Wee Hooker nailed it but then thought it thru. Now, I think a standard breaker that controls that circuit is going bad and heating up, then cools, then heats up, then cools, but never actually trips. IMHO, you should identify that breaker in the entrance panel and replace it with a new one. Cheap and easy to do. There is no reason for a GFI to be used on the circuit you described unless there is also an outside outlet that you didn't mention. But then anything is possible. I would check them all against the original circuit again. ............ Big Cholla