There is something up for sure with the Gen/wiring. One thing to note is that ALL the outlets are on a single 15 amp breaker. So if you have a 1500 watt heater, there is practically no more room for anything else. When temps are above freezing, I'll run one 1500 watt heater using the microwave circuit, then another one using the passenger side outlet. Helps lower our propane usage when hooked up.
I believe the Onan Gen has a 3 year warranty, but I think your issues is with how FR installed it. Ditto edm's question, is it tripping any circuit breakers? What do you mean by "shut down"? If no breaker is tripped, is your microwave still on? That usually tells me if the generator is putting out 120V or not.