May be early onset of the electric fuel pump failing as it gets hot. Be sure to ensure the fuel pump is pumping fuel to the carb by pulling the hose off the carb and watching for adequate flow. A faulty electric fuel pump can often only show symptoms or act up after it is warmed up. Sometimes it may run for 10 or 20 minutes and just shut down. Check for fuel flow immediately upon stalling if this is your symptom. Mine would shut down after 20 minutes and not restart for awhile. I pulled the hose off the carb immediately and noted there was no fuel in the line and it would not pump fuel while holding the start switch on either. If you are mechanically savvy you can disconnect the hot wire the positive wire (red) leading into the fuel pump and connect it with 12 V and see if it pumps fuel out the hose also, but be careful to capture the fuel coming out the hose). Once cooled down it pumped fuel in a weaker than normal stream, but when hot after 10 or 20 minutes it quit pumping causing stalling of the generator. Replaced the fuel pump (and new filter while at it) and everything worked fine again on my 1995 Onan. Much stronger fuel stream noted too from the hose.

This sounds like overheating. These small generators don't have overheating protection, but if a low oil pressure or low oil level is present it may be the reason for stopping.

Check the oil level in the starting conditions and again when it stops. It may become under the "stop" level and after some time the precipitated oil has reached the "start" level. The same may be with oil viscosity and oil pressure.

Try to add some oil or change the oil with bigger viscosity.