There can be several things causing this. The good news it the genny knows a heavier draw is coming and kicks in. The easiest thing up front I'd suggest is make sure all tune ups are done to the genny. Make sure your plugs are good, your oil is clean, and air filter is clean. Put some marvel mystery oil in the fuel. Remember when a generator has a heavier load, the engine is under more strain. I'm not saying this is the cause, but it is always a good place to start diagnosing for minimal costs (plus it's good for the genny)