What is indicated by a well pump temporarily recovering when shutting off the power for several hours?
In this particular case, when the well drillers came over, they agreed with many of the comments: it was either a bad pump, or a leak. They ruled out the leak after testing the water pressure directly at the well head. The submersible pump was over 275 feet down (at the very bottom of the well). The pump was determined to be as old as the house: 36 years old, and only 0.5 horsepower.