Is cycling on and off too often. This is probably caused by the loss of precharge air pressure in the water tank. We are talking about an air leak, not water leak. IF you have the type of tank that has a bladder in it, it may have to be replaced. It is what is called "waterlogged"
Your "plumber" should have known this. Perhaps he isn't familiar with well pump systems. I would call someone that installs well systems, they should be able to help you.