The plumber is correct but what do you think is the cause of the problem?
If you have a jet pump, in the house or above ground, you are running the risk of losing prime because you are shutting off the pump. If that happens you probably will not be able to reprime the pump and will be out of water until you fix the leak. It may be the foot valve for a jet pump, or the check valve on a submersible pump, in the well on the end of the drop pipe in the well.
Call a pump guy or well driller or only a plumber that is capable of pulling the drop pipe or pump out of the well to check where the leak is.