Plumber Rick probably hit your diagnoses right on the nose with the foot valve. As soon as the pump shuts off at high pressure turn of the feed valve to the house. Watch your pressure guage (if one is installed, if not silently curse the so and so who installed your system and install one)If the pressure in your system falls back to where it has to refill your bladder tank you probably have a faulty foot valve or a leak in the pipe between your foot valve and the pump.
Theron was also correct that the bladder in your tank may have failed leaving no room for storage, in which case event the smallest leak as from a faucet drip or bad flapper will cause your pump to cycle constantly.
One other thing to consider would be a very old system that simply relied on the air being compressed on the top of the tank and not a bladder. Usually these are upright cylinder type of tanks. These have an air chuck which can allow for more air to be reintroduced into the system. This is not to be confused with the smaller bladder tanks which also have air chucks to properly charge the tanks to within 2 psi of the desired high side pressure.
Work hard, Play hard, Sleep easy.