I have 2000IS that I've only ran steady for 3 times. All of a sudden when using it on the 3rd time, about 2 hrs of run time I started to notice the generator sounding like it was about to die, and then idle back up. Then finally it would quit. The gas was new but I changed it out anyway. What it's doing now after setting a night, is it will start up, idle for about 25-30 seconds and then just shut off like someone turned it off. This is without anything plugged in. When it runs for that time the AC light is on the oil light is off.
koscoves, The oil light will only illuminate as the engine RPM is shutting down, or when the recoil starter turns the engine immediately afterward. You can be low on oil and the oil-alert system is shutting the engine off. This can be made worse by running your Genny on uneven ground even if the oil level is OK when checked on the level. Also, as an observation, not a criticism, I am not feeling confident we are getting proper descriptions with "sounding like it was about to die, and then idle back up".
There are other conditions that can cause your running problem. Choke use/adjustment. Water in carb floatbowl. Idle control motor away from the engine off full throttle setting position.