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.
Computers manufactured by companies such as IBM, Compaq and millions of others are by far the most popular with about 70 million machines in use worldwide. Macintosh fans note that cockroaches are far more numerous than humans and that numbers alone do not denote a higher life form. -NY Times 11/91