From one newbie to another; Details on the brand, model, etc. of the generator will pull out the experts. I had a question about my GenSet not long ago and got great info.
My only contribution is to make sure the fuel level in your tank is above 1/2. The generator draw tube is designed so that it will run out of fuel, but you'll still have enough left in the tank to drive quite a long distance. If you've got plenty of fuel, there's the possibility that one of the fuel lines has a crack that is causing the fuel pump to suck air.
Enjoying the simple life w/a 1994 Winnebago Brave 31RQ (A). Past RVs; RoadTrek (B), Starcraft Pop-up, Coachmen (C), MinnieWinnie (C) and an American Something-or-other (TT). Started it all off as a teenager in a 1964 Apache Pop-up we named Wag Along.