Keep in mind the trip is 4-5 ma. It doesn't take much to trip a properly
functioning GFI

My list of the trouble makers (in order)
-GFI breaker getting fussy in it's old age.
-Moisture or fuzz growing in one of the outlets
-Moisture in the wire
-Rodent damage

Pull the wire off the breaker, see if it still trips. While it's off,
pull the neutral wire off, run an ohm check on black to ground. Anything
less than several hundred K ohms is suspect, 25,000 ohms will pop the
GFI. Disconnect everything on the circuit, same readings.

Karl Townsend wrote:
I have a circuit protected by a GFI circuit breaker that has failed. So far,
I eliminated anything plugged in or switched. Also determined that the
circuit is fine with a standard breaker and draws no current. So, I left it
this way for now.

Its impossible to check the actual wire runs behind the sheetrock. Is there
anything else to check as a possible source of the trouble?

Karl