If the pump is running but flow and pressure drops to almost nothing, the problem is that water is not getting TO the pump in sufficient quantity to keep up with pump output. The most likely cause is a leak in the intake line which allows the pump to suck air instead of water. A tiny pinhole can cause an amazing loss of suction! Another possibility is that the tank end of the pump intake hose is partially clogged. Once the pump delivers the water that is in its intake hose, it can no longer get enough additional water to keep up with demand, but when the demand stops the hose slowly refills with water and it is ready for the next time.
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL