Another possibility is a leak in the intake line at about the level of the water when pump looses prime.
When I hear pump loose prime, I think of pump running, pumping, until turn/cycle off. When next comes on, no water. Put enough water in tank for it to prime, run without shutting off. Does it at some point start putting bubbles in the stream? If not, then it is likely a small leak that is letting air in, that allows water in line drain back to the tank. If water level is at or above the level of leak, water stays in line.
