Could be a leaky check valve. Here are some things to check out. You can skip steps 3 and 4 for now if you want to get at the leak problem right away.
1. Verify that you have a good gauge.
2. Check the time to fill the tank. Shut off all usage and then run the water until the pump starts. Measure the time in seconds to pump to shutoff. Record the time and start and stop pressure.
3. Measure the air pressure in the tank with a tire gauge. It should be the same as the water pressure gauge. Differences are gauge error. Don't worry about small error but notice the difference.
4. Check the air in the tank. Shut off the power to the pump and run water until there is no more pressure. Then, using a tire gauge, set the air pressure in the tank to 2 psi LESS than the pump-start pressure. Take into account the pressure difference you observed in step 3. If the air is off a bit, don't worry too much but plan to add some air later.
5. With all water demand off in the house, run the pump until it shuts off. Then watch the gauge for about 15 minutes. It shouldn't change much if it changes at all. If it loses significant pressure, then you have a leak somewhere.
6. Possible leaks are:
a. Check valve at the pump or in the suction pipe. If you have a submersible, the check valve is probably in the pump. If you have a shallow well jet, it is probably a foot valve at the bottom of the pipe. It may be in the pipe near the tank. It will probably be a brass cylinder, perhaps with an arrow on it pointing away from the pump.
b. Leak in the pipe somewhere between the tank and the well.
c. Leak in your supply system. Least likely because you would notice it, unless you have an irrigation system that might be leaking.