Generator Stalls out

Had a similar problem. Tried a new pump and filter, still would stop sometimes. Eventually found a crack in the rubber section of fuel line on top of the gas tank. Could just see it looking through the gap with a flash light. Had to drop the tank down and replace it.

I will have to try both of your suggestions. I have the same issue.

Low oil? They all have a low oil shut-off, and if you are right on the edge, it would run fine sitting in the driveway, but hit a bump on the road, and the low-oil shut-off could be triggered.

How old is the unit? Most of the time, this behavior points to the Onan fuel pump. They'll run for 10-20 minutes, then die.
Odd yours stays running while parked, but fails while underway. It could be heat or vibration that causes the pump to quit.

Next time it dies, park, kill other sources of noise like your engine, then try to prime it. After a few seconds on prime, the pump should start making noise. If it's silent, then it's most likely the pump.

Let us know what you find.