GFCI's generally require you press the reset once they loose power, which essentially happens when you disconnect shore power to travel, etc.
If the problem only exists under generator power, start at the breaker box /transfer switch where thew two power sources meet the coach wiring system. The generator likely has a poor connection on the neutral / white wire.
If nothing there, I would check your output voltage of the generator. You will need a basic voltage tester that you can plug into a receptacle while the generator is running. You should have somewhere around 114-125 volts. most dumb appliances such as a coffee pot, lamp or cell phone charger wont notice a variation, but the GFCI has circuitry that could sense a low or high, "out of range" voltage and will trip.
This will indicate a faulty voltage regulator on the generator.
I expect if there are problems with wet or damaged receptacles downstream from the gfci, it would trip from both power supplies, not just the generator.
Happy hunting.
Rod
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