PROBLEM SOLVED! Shore power cord had been pulled from outlet by teenage son on a riding mower (blade not spinning...whew!) When the plug was jerked from the outlet the plastic outlet face at the ground terminal apparently broke but wasn't noticed. Son reinserted the plug and all worked fine until the weight of the power cord and the lack of good contact due to the broken plastic caused the ground to fail. A new outlet for $7.61 and we're good to go.
Thanks for all of your suggestions, especially those that recommended I begin at the breaker box and work out towards the camper. Otherwise I'd still be replacing camper outlets and fighting with the converter unit.