If you have a submersible pump it could be that there is a hole or split in the pipe between the pump and the well head. When this happens you will only get some pressure when pump is running since most of the pressure could be lost back into the well. This is more common when black roll plastic pipe was used to install the pump system. Another cause could be that the pump impellers have been damaged by debris(usually you would have noticed a gritty type debris in the water at times)thereby reducing the amount of pressure that could be produced to lift the water to the tank.
One note about the hole in the pipe situation, if you do not have a check valve installed at the pressure tank and you have a pressure gauge that is working you should notice a pressure drop when the pump is turned off. If the hole in the pipe happens to be above the well water level then you will sometimes get air spurts when the pump kicks on again.
If it is a jet pump system then it gets a little more complicated. It could still be a hole in one of the pipes but frequently this will cause a loss of prime. Other problems are: worn impeller, debris in venturi,footvalve not working properly and debris or out of adjustment regulator(these usually are located on the pump housing and normally have an adustment screw. It regulates how much water is forced back down the return line to the footvalve assembly). Hope this gives you some ideas on what to check out first!