Interestingly, when the harbor replaced the outlet, they told me exactly the same thing happened to another boat just a few boats down, at almost exactly the same time. Makes me think there was some kind of power surge or brownout or something.
power surge or brownout don't cause that sort of issue. it's just a coincidence that it happened when yours did. when you run electric heaters off shore power for extended periods you'll burn those plugs up. it's just the way it is. i've been living aboard for close to 30 years now, and i know, if you run on the edge of your 30 amps all winter you'll have trouble. all the trouble spots have been mentioned. wire and buss bar on the pedestal, receptacle, breaker, your cable, the wiring behind your shore inlet. the plugs are rated for thirty amps, but if you load them to that they'll fail. we're stuck with them though, it's what every marina has.