Question: Does this outlet, and the ones it feeds. have their own circuit breaker? Nothing on this breaker that is not GFCI?
NO; I tried
Yes: Visit your electrical supply and pick up two things
1: Standard 15 amp DUPLEX recptical to replace the GFCI Or a 15/20 if the GFCI has "T" shaped neutral connections.
2: A GFCI/Circuit breaker combination.
Remove the breaker and replace it with the combo (requires a bit of work but should be simple for you) replace the GFCI with the standard outlet.
NOW: you still have full GFCI protection.. Only now it's the breaker that is the GFCI so you need not ask "Did I trip the GFCI or did I trip the BREAKER, they are one and the same.
Question: Why do they not use these breakers at the factory????????