On some setups, and this problem sounds like one of them, the exit point of the tank that leads to the intake of the water pump, sometimes have a pre filter the shape of a nipple that is part of the exit plumbing. This nipple is a screen material probably stainless steel to eliminate corrosion. Over time the inside of the water tank develops a skin like material that is not harmful, but clings to the wall of the tank. Constant filling and draining can can shake loose some particles of material as the water level drops and float to the discharge point of the tank plugglng the screen on the inside of the fitting. Removing the fitting at that location will reveal I think, the culprit of your issue. It will come out as one piece and is easily cleaned.