Water Pump that kept cycling on/off

I have spent the past year trying to solve my water pump problem where the pump would keep coming on / off. Obviously you would think that a hose somewhere was lose and need to be tighten. I did that and it still came on/off. Next you might think that the faucets needed service. So we did, we took apart every faucet, cleaned all o-rings and re assembled them, even the shower units. Still, on/off! What the heck?

So while anchored off Cuttyhunk, we ran out of water, so I thought. The pump would run but no water....So, off I go in the dinghy to get 10 gallons of water, bring it back and pour it in. Sure enough, the pump runs, but no water. Great, the pump must be bad, no worries, I have a new spare.

After installing the new spare pump, guess what? NO MORE ON/OFF! Yup, it was the pump all along that would not hold pressure. Now after a year of trying to fix this, it is not fixed.

So, if your water pressure system does not hold pressure, and your pump is old like mine was, maybe it is the pump, and not the fittings.

We installed a PAR MAX 3.0
Model 31395-3000
50 PSI (this concerns me, because the old pump was 40 PSI)