My water well pressure switch seems to stay open after the water pressure reaches it's limit. It won't close again once the pressure gets down to the re-start level. Why?

Sounds simply like a failed pressure switch, they don't last forever but are easy to replace.Part 1 of 4: How to Replace a Well Pump Pressure Switch - YouTube

Will the control box shut the pump down when it reaches the cut off point? Have you checked them small tube the runs between then pump and the control box for a blockage? Back to you, Tom

Switches are cheap, so it's OK to replace it on a guess. Whatever you do, replace the little pipe leading to the switch. They clog easily. In fact, that could be your problem.