We have a gen at home and we had a similar issue. On ours, it turned out to be the carb. Worked great until you shoved a load on the motor. In our case connecting an appliance that took some load added demand to the engine that carb could not fill and as such, the engine died. Rebuilt the carb and the problem went away.
Basically, the carb could not get enough fuel to the engine when a demand was placed on it. One thing though, in our case the breakers did not throw.
Eric
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