CRNG wrote, on Sat, 28 Jun 2014 19:28:54 -0500:

I think you are correct.
Your pumps are shutting down because they are running dry.

I'm pretty sure they're running dry, because one, for sure, is only
running for less than 2 minutes before shutting down, even after
having been off for five hours!

Here, you see it has "tripped" by the red light:
https://c2.staticflickr.com/6/5487/1...08be46fd_b.jpg

The other well, after I allowed it to refill for 5 hours, lasted
22 minute s, but I timed the water meter and it was going at about
10 seconds faster than 5 gallons per minute at first, then about
at the halfway mark it was about 15 seconds less than five gallons
a minute, until it finally shut down at 22 minutes, averaging at
about 4 gallons per minute.

But, that was after a 5 hour quiet period. In practice, the well
*tries* to pump all day so the 'rest' period is only a half hour
or so between shutoffs.