I think you answered your own question. It sounds like the foot valve is leaking back.
If you closed the valve after the tank, and it still fell, the foot valve is leaking, or there is a pressure crack in the drop pipe.
As you pull the pipe to change the foot valve, keep a close eye on the pipe, as there may be a split or crack.
The valve before the tank should never be closed. That will make for a very short life for your pump. Cycling like it did when you closed the valve before the tank will kill a pump.