We installed a new water pressure tank, gauge, and pressure switch. The tank loses pressure when not running water. What could be the problem?

When you say "Pressure Tank" are referring to a bladder or a galvanized pressure tank? (see images). What is the cut and cut out of your new control box? When you lose pressure do you have to prime the pump to get it back?
Why did you have to install a new tank and control box?
Because of a problem that existed before you installed the new parts?
In short, you haven't supplied me with enough information to work with. Please answer my questions with as many details that you have.
Regards, Tom

If you're losing water pressure when no water is being used, there is a leak somewhere. Could be a checkvalve, could be "upstream" toward, or in, the house. Do you have a shut off valve to the house? If so, turn the house off and see if the pressure continues to drop. If it does, then you likely have a checkvalve/footvalve problem.

Is your pump in the well or above ground?