This sounds to me like a minor neutral-to-ground fault on the load side of the GFI receptacle. Not necessarily enough to trip it, but enough to make it "think about it". I've found things like cobwebs in outdoor receptacle boxes to be just enough to cause phantom problems depending upon the humidity level. This minor amount of leakage is impossible to detect in testing.
Then again, how much cable length is on the load side of the GFI? If it's more than 250 feet, that alone is enough to cause them to malfunction even with no load. 250 feet sounds like a lot until it zig-zags all over the house to hit all of the bathrooms & outdoor receptacles. I don't even like to see 200 feet on the load side myself.
Fountain pumps are notorious for causing nuisance GFI activity. Inherently, electric motors have a small amount of leakage to ground and they will have you pulling your hair out since this leakage only occurs while the motor is running. Any kind of small motor load can cause this wacky activity on a GFI though, not necessarily just pumps.
Just a few suggestions. Hope this helps.
