Had a similar problem with our Onan 4000.
Trouble shoot the fuel pump by using the priming pump switch (the on/off switch at the genset, not inside the RV), and prime the engine. You will hear the pump running...a dull clicking sound.
Run the engine until is shuts-down.....then try to immediately prime the pump again....if you don't hear the pump running, it's your pump!
(basically, the pump is overheating, tripping an internal safety...which after a few minutes will reset, so you can start the engine again).
You may also want to replace the fuel filter when/if you replace the fuel pump.
If the pump appears to be working....you may want to disconnect the discharge side (to the carburetor) and attach a hose, so that you can check to see what kind of flow you are getting. It could be that there is some blockage in the fuel line?
If all is good...you may have some issues with the carburetor....have you tried running any SeaFoam carb cleaner through it? Get a gallon of gasoline, add the SeaFoam (available at Walmarts or Auto parts stores), and use a pick-up hose to the fuel pump suction side.....prime the engine, and start and run until you run out of fuel. That should help clean the carburetor, and get the engine running better.
Good luck:)
