Submersible Well Pump Quits Under High Demand
On a submersible pump, the motor is cooled by the water.  If the pump starts sucking air, water is no longer flowing around the motor, the motor overheats.  

A well in operation produces a cone of depression in the surface of the water level in the aquifer.  If the aquifer is very permiable, the cone is shallow.  If you have a restricted aquifer the cone is deep.  Pump long enough, and you have a say 30 foot diameter zone that the entire aquifer is drained out, with a few inches at the bottom streaming into the well.  Stop pumping and the aquifer levels out.

I suspect that what is happening is this:


You start to pump.  
After a while, the pump is exposed.  
It warms up, and it's thermal protection shuts off.  
You reset it.  
The aquifer starts to fill.
Repeat.


That the 5 minute break is enough for normal operations to resume means that the aquiver is almost capable of keeping up with the pump.

If I'm right, there is nothing wrong with your pump other than it's too big for your well.

Test for this:

Start with having ALL the water in the house shut off.  Someone taking a shower or flushing a toilet will mess up your numbers.

A:  When you run a garden hose wide open, how long does it take for the pump to cut out.  This is going to be a murky number because of the pressure tank.  If you can isolate the pressure tank it will be easier.  Lets call this time Wi  for wide open isolated tank.

B:  While this is happening, time how long it takes to fill a 5 gallon bucket.  With a typical garden hose it will be about 25-50 seconds.  This is Ti

C:  The pump cuts off, and the water flow stops.  This is Pi the time from when you turned on.

Give the well a rest.

D: Start it up again, but close the garden hose tap enough to increase Ti by about 20%  So if it was 25 seconds before, it now takes 30 seconds.

If my theory is correct, your well may be happy with this new value and will pump all day.  Record the new time it takes for pump shut off.

Repeat the rest, and check, adjusting the flow to increase the time by roughly 20% increments until the pump keeps running/

Let's suppose your final  time was 75 seconds.  75 seconds/5 gallons = 15 s/gal.  Invert that to get 4 gal/minute.

Go to your local well supply store and ask for a 4 gpm flow restrictor.

Install that somewhere between the pump and the pressure tank.  Do it in a way that you can take it apart later.  You may have to swap it for a 3.5 or a 3. 

If you can't isolate the pressure tank, it gets a bit messier.

Start by waiting for the tank to reach full pressure and for the pump to shut off.
Turn off power to the well.
Go outside, and open your tap, timing how long it takes to empty the pressure tank.  You can use any arbitrary cut off point.  You just want to be consistent.

You want to be able to recognize when the pump goes off.  This time is subtracted from the running time of the pump in all the tests above.

Whenever you start a new test, let the pump come up to equilibrium with the tank before you do any timing.  If it takes 3 minutes for the tank to drain, then wait three minutes after you turn the pump on to time your 5 gallon fill.  You may want to do several 5 gallon fills to see if you are getting consistent timing.



In operation you won't notice the flow restrictor.  The pressure tank will still hold a shower or two of water at normal pressure.  (Assuming you don't have one of these tiny ones) If you use water long enough the well will cut in, and you will get only the 4 gpm from the well, instead of the 6-8 gpm from the pressure tank.  Note that most showers now are 3 gpm.  A toilet may be 3-5 gpm for a minute depending on how old it is.  

You will notice it watering the lawn.  You will get several minutes of high pressure watering, the tank will drop to some lower value that 4 gpm can keep up with.  This will mean you have to adjust your sprinkler after a few minutes, or use lower flow sprinklers.