There are a number of possibilities. Usually, the oil-lubricated pumps don't fail, it's usually something else.
While it's running, feel around (careful, some parts are pretty warm!), and possibly you can find the leak. Concentrate on the piping from the pump to the tank. Make sure the unloader valve is closed. Feel around the pump cylinder for a blown gasket.
The intake filter could be clogged as well.
Once it builds up any pressure, does it hold it after it's turned off? If so, the problem isn't with the tank, it's either the pump or piping.