Compressor repair help
The little bit of air that blows off when it shuts off is normal; that is the unloader, releasing pressure in the discharge line between the head and tank, which it is supposed to do. Running an air compressor on a generator is never a good idea, in my opinion, due to the initial current draw at startup, which can easily double the current draw, or more. I am out of ideas, other than the fact that I still suspect that the motor is kicking out due to an inadequate power supply, the pump is siezing, or the motor itself is bad. The fact that the contacts in your pressure switch are not moving pretty much confirms that fact, in my opinion. If your house has older wiring, maybe haul it to a buddy's, and see how it works there. Otherwise, good luck. Maybe someone else will have some other ideas.