Your cut-in and cut-out settings, and air pressure sound normal. You
must be losing water somewhere.
Do a test. If you have a turn off valve at the pressure tank (that
allows the water to go out of the tank and into your home plumbing system),
turn it off. If not, just be sure that no water is turned on in your
Let the pressure build up to 53# max, then quickly shut off the electricity
to the pump. If your pressure goes down noticeably in 5-10 minutes, then
you clearly are losing water somewhere in the system.
I don't know about jet pumps, but I assume they have to have some sort of
checkvalve. Either way, I would bet that you have a checkvalve
somewhere in your system. I understand there is frequently a checkvalve
right at the pressure tank.
If the pump checkvalve or a checkvalve at the pressure tank are bad, it
will make your system contantly leak water, and cause the constant recycling
that you are seeing.
I hope this helps. Let us know. There are plenty of people on here that
know 100 times what I do about these things.