None of the following suggestions are in order of importance - just random thoughts.
How many hours on the generator? If a lot, you could need the injectors serviced.
Have you been running it a lot with a low load? It's possible that there is soot buildup that is just burning off under higher load. Run it at load for a while and see if it goes away.
Check the frequency and voltage with and without load to see if the load is drawing them too low. You may need to adjust the governed speed to bring these back up.
Is this a capacitor controlled head
? If so, the capacitor could be getting weak and dropping the regulated voltage or causing the head
to put a greater load on the engine
. They will do this for a couple of weeks before failing completely. Try changing the capacitor and seeing if the problem goes away.