If the pump is failing, or has some sort of a
screen that is plugged, the fuel flow would be insufficent to allow the
engine to run at speed once the initial "charge" is depleted.
Think of it like this, you have a garden hose and just barely crack open the valve. When you
plug the end of the hose the pressure in the hose builds up slowly to the same pressure as the
water in the pipes, when you unplug the end of the hose you get a burst of
water that quickly turns to a trickle.
Now take the fuel going to the
engine. If the pump is failing or has a fuel restriction somewhere, The
generator is supplied with sufficient fuel pressure for a short duration then begins to starve. I'd be willing to bet you have either a plugged
screen in the pump, or a pump that is on it's last legs.