Don't go below that fuel level?
Sounds like you may have a split in the fuel supply hose which is getting air into the line. While the split is in fuel, it will continue to pump without problem as it will be sucking fuel in. Once the fuel level drops below the split it will be sucking in air from the tank and not fuel.
Take the pump out and check the connections to make sure they're secure and that you haven't got any splits. Worst case scenario is to buy some fuel hose off ebay and replace the lot to be sure - shouldn't cost you more than a tenner.