Have older Honda 3500 watt generator motor will not stay running?

I don't know if this will help you, but I have seen this on newer Honda Generators. The new ones have a small slide switch on the gas cap that lets air in. It can be turned off for travel. However if it is left OFF when the engine is started it will cause a vacuum in the fuel tank and starve the engine. Take your gas cap off and see if the air vent plugged (If it has one) This may be the problem. Or put about 1/4 tank full of gas in the generator and see if it keep running without the gas cap on. If it does, it's a plugged air vent in the gas cap.