Where is the leak coming from? If it is from the nozzle of the tap itself than get a new tap. Cut the serving tube just behind the old tap, heat the new end of the serving line with some steam and put the new tap on.
Another idea if you are losing that much beer is that your serving line might not be the right size for the picnic tap, although this seems pretty unlikely since then it wouldn't be the right size for the adapter on the keg post either. Does the tube fit very snugly around the picnic tap, to the point where it bulges the tube a bit and you can't pull the picnic tap off?