My Generac electric start generator starts perfectly but quits after about 10 seconds. Then it won't start again until it sets for about 1 minute. After a minute it starts on the first try, runs 10 seconds and then quits again.
My first thought was a sticking float in the carburetor. New carburetor - same thing. It turned out to be the oil pressure sensor switch stuck. The control board has a 10-second timer that kills the ignition after 10 seconds if oil pressure is not detected by the switch.
Good info, it will likely apply to others too.