Not knowing your mechanical ability, there isnt any way to know if you can fix it yourself. The governor isnt mentioned in the owners manual because its not a maintenance item.
You should have a manual, or at least an exploded parts diagram of the governor mechanism to guide you. But before I tore into it I would look around by the throttle lever for some kind of electrical solenoid used to control throttle. Youll see a throttle lever and two speed set/lock screws. One screw is high speed set, other is idle/low speed set. Most diesel generator engines have both screws tightened up against the lever so it will only run at high speed, IE;the lever wont budge. However, yours may use a solenoid to draw the lever over to high speed. Lacking that, your problem is likely internal
I would guess a diesel mechanic would want some big bucks to deal with the injection pump, so if you can figure it out you can probably save a substantial amount of money. My guess would be something came off the lever control arm, possibly a broken spring or something, possibly why it initially revs up then falls back to low speed.
Every time ive taken one apart I have been amazed how simple they are. Youll likely find the same thing. Its not rocket science. When you re-set governor high speed, use a meter with AC cycles, and set as close to 60 as possible, checking no load, and fully loaded.
