generator problem

Your genny problem could be caused by a number of things. as someone who works on these things, if you posted complete model/spec/ser. no. I may be a little better able to help. Most Probable cause is fuel pump or control board (the control board feeds power to fuel pump) To determine actual fault, you need to be able to test fuel delivery as soon as shuts off, and check for power to fuel pump from control board.
Onan has posted two different groups of fuel pumps that had higher than normal failure rates. Need to have manufacturer's date code from pump to determine if yours might fall in one of these dates

also, when your unit shuts off, it should display fault code (series of light blinks at start stop switch) your operators manual should tell you how to read these codes, and this can help to identify system (fuel, ignition, voltage output, etc)that is at fault

This summer, after having the oil changed on our generator (Onan 5500) it would run for a while and then quit, especially while driving. In looking at the generator, I found that the mechanic did not attach the cover correctly. Upon reseating the cover, the generator worked fine for the rest of the summer. This fix seems silly, may not be your problem but it worked for us.

Probably have the same unit in our 2002 32V Itasca Sunrise. changed the air filter, both fuel filters, and the oil. Worked fine until I put it under load, then it would shut off after about 20 - 30 minutes. Put in a new fuel pump and fixed the issue. Just got back from a trip to the desert southwest, boondocked with no generator issues.

I had this problem, it was cause by low fuel level. My generator shuts off when the fuel gauge falls below 1/4 tank. It will start, but stops a few minutes later.

Check the fuel filter or the fuel pump.

I had a similar problem with a 4000K unit. It turned out to be electrical connections. If you take the cover off, there was a large plug with a lot of wires. Gently pried apart, sprayed we tuner cleaner, plugged and unplugged multiple times, back together and problem solved. Don't know if this could be your problem but solved mine and symptoms the same. Just be very careful prying apart as multiple tiny prongs in plug as looks like main connector. Good luck.

Fuel filter.

SORRY: the generator is a onan HGJAC 5500 in a southwind 32v motorhome

And check the oil level.

Unless you give us more info we can't help a whole lot.
Change your fuel and air filters if they have not been changed recently.
If you don't know when they were changed, change them.
Start with the simple easy things.
Is there sufficient fuel in the tank?