I have almost identical problem. It runs good for a bit then starts missing then just quits. I am suspecting a solid state part in the control circuit getting hot after powered up. There is a circuit board that is tied into the ignition ande oil pressure cutoff switch. I'm looking for a parts manual and/or troubleshooting guide. Will post again with aqny progress......
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RE: doesn't stay running
Same problem, had to replace carb,had a hairline crack (from heat). solved problem.
Carb.$68 Labor $35 and Generac will not help you, they do not care!!!!!!!