When I leave the cottage for a day or so, I will turn off the power to the pump. When I return and turn the power on, I have lost pressure, but still maintain prime in the pump. What's wrong?

When you turn the power back on, does the system pump back up to operating pressure? If so, then you have a leak somewhere, most probably between the pressure tank and the house.

When I leave and turn the power off, I also turn "OFF" the green valve so the water in the cottage doesn't flow backwards. When the power is turned on, the pump runs but the pressure does not come back up. Turning the green valve "ON" I can hear water running into the pressure tank that sounded empty (hollow). Now the pressure valve starts to come up to normal. I think the pump cycles sometimes even though water is not being used as the pump is a little distance from the cottage and I can't hear. Where is the water going from the pressure tank to make it sound empty?