Make sure you are measuring the air pressure when the tank is drained of all water. Any other measurement will be wrong if you do not do this correctly.
The first thing I would do is clean out the inlet pipe for the pressure switch. Since the switch is probably damaged by short cycling, I recommend replacing it. If you install a 40/60 switch the air pressure in the tank with no water in it should be adjusted to 38 psi before turning the system on.