TSPatt,
Welcome to the forums!
Do you have the manual for your generator? Is it flashing any particular code?
I don't have any experience with that particular generator, but I do know that some of the gas Onan's were very temperamental about their oil levels and even oil viscosities as things warmed up. Yes, I have one! LOL
Does your generator have an oil level sensor/switch? If so, make sure the oil is at the proper level.
On my Onan, it would often shut-down when running the multi-viscosity oil spec'd by Onan for hot weather. Only when I changed to a straight weight (30, I think) did the problem stop. But I still have to keep the level up or the sloshing while driving will often trigger a "low oil" condition and shut-down. Usually, it's only a problem in hot weather when the oil is thinnest.
Hopefully some others on here will have more specific information about your model.
Good Luck,
~Rick