Double check your LP pumps. I had the same situation and I thought the HP pump was bad but turned out to be the LP pumps. Sounds like you do have an issue with the HP pump wiring if you can jump it and it works. If it still won't stay running check your LP pumps.
Just unbolt the LP pumps from the powerhead and pump your fuel bulb with your hand on the back of the LP pump. If you feel gas LP pump is most likely bad. Typically, you won't get much more than one season out of the LP pumps.