I don't think the well is running out of water. I think the overload in the motor is tripping. It has a built in overload that resets itself after a couple of minutes. I also suspect that cycling on and off is causing the overload to trip. A 1.5 HP pumping from 200' can produce 16-18 GPM. Even with an 80 gallon tank that holds 25 gallons of water, that pump can still cycle on and off a lot. If you have a smaller pressure tank, it cycles even more.
You need a clip around amp meter or look at your electric meter when the water stops flowing. If there is no amperage going to the motor then the overload has tripped. If there is still amperage going to the motor, then the well is pumping dry.