My first though was that the bottom backflow valve had gone bad, I had this happen to me, but the pump still got up to pressure, but as soon as it shut off, the pressure would drop and the pump would come back on. It also caused a lot of air to get into the system.

I favor the hole in the pipe theory because that could limit the pump pressure and since the pump is not shutting off, it wouldn't get any (not much anyway) air into the water. I disregard the worn pump because if the owner manually shuts off the pump, he looses pressure, but the pump may be worn out, but I don't think that is the root cause of this problem.

Since the whole pipe has to be pulled out anyway, if the pump is old, it might be a good time to replace the whole line and pump and not have to worry whats next.