My well pump and system hold pressure just fine. When my well pump starts, the pressure drops to 2 psi and then takes approx. an hour of the pump running before it stops running at 44 psi. During the time that it drops to 2 psi, there is no running water available in the house until after the pressure builds back up. Why does my pressure bottom out to 2 psi when the pump starts?

It could be a number of problems, but I am guessing that you have a hole in the line somewhere in the well, probably underwater that most of the water is pushing out of. If the pump is pushing 35 gallons per minute, it may be losing 34 through the hole. It could be that you have a restriction in the line that is severe as well, but that would normally take place in a house filter that is after the pressure tank, and the pump wouldn't run any longer than normal.

I would get a plumber to come take a look, but you may be able to narrow down the problem if you can take the line apart at a union and let it pump unrestricted and see what your pump's flow rate looks like.