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.