Short cycling of a well pump is a fairly common problem. One of the most common causes of well pump short cycling is a loss of air charge in your well pressure tank. If the bladder becomes damaged it fails to hold pressure properly and the result is a the pump going on-off, on-off.
When your water tank is failing to hold the proper pressure, it usually must be replaced. Waiting to replace the pressure tank can only make the problem worse as the short cycling causes undue stress on the rest of the system.
One of the common problems that results from ignoring a failed well pressure tank is a burned out pressure switch.
Additionally the constant short cycling of a well pump can cause a failure of the wires that reside in the well casing.
If your well pump is short cycling, the best thing to do is to bring in a qualified well pump contractor as soon as possible. The cost of replacing a well pressure tank is certainly less than the adding the cost of replacing a pressure switch and possibly the well pump wiring.