Water Pump constantly loses Prime

[njk53]

I didn't see a statement whether or not you are running a coolant recovery bottle (CRB). If you are running a CRB, the outlet on the bottle should be at the highest point in the cooling system. This will help replenish coolant in the system after you shut the car off. When a cooling system is at temperature/pressure, eveything expands and pushes the coolant into the CRB during operation. When you shut the car off a vacuum occurs pulling the coolant from the bottle back into the radiator filling it. Also, make sure all of your cooling systems hose connections are tight. Leaks will prevent the vacuum event.
From your description, it looks like when you shut the car off when the water pump is working, the coolant that got pushed out of the system during heat expansion isn't being vacuumed back into the system.