I doubt overheating is the problem, since it's not a high-performance engine full of electronics crammed into a cramped engine compartment, like the crap BMW manufactures. More like lack of maintenance, improper oil change routine, even using incorrect oil.
My money's on the electronics failing, but not because of overheating. These generators are designed to run for extended periods of time, even at full output. Spikes and surges in this output, or regularly overloading the generator, that's the bad shit.
And it's actually not even 6000 watts, it's 5500. 6900 starting/5500 running, strictly on gas.
Edit: I don't think this is designed to provide enough power for what, 8 people? 7 people and a leech? Whatever. It should be more than enough to complement a primary power source, not for being one.
4-stroke running at 3600 RPM, that's not likely to overheat.