Ran in to a similar problem about a year ago with a 56 Chevy car running a stock 235. Everything from the fuel pump itself to the cam lobe was blamed. As it turned out the short rubber flexible fuel line that attaches to the tank fitting did not have a clamp on it and as time went on the hose simply lost its snug fit on the tank barb allowing the pump to pull air instead of fuel. Since the hose connects at the top of the tank the car never leaked any gas to give a hint of the problem area. Interestingly enough one know it all temporarily mounted an electric fuel pump and the car ran fine the entire time that pump was being used. The explanation of course is the electric pump moved a lot more volume than the stock pump so the mix of air and fuel was enough to keep the carb full and the air drawn by the pump was simply vented out the carb bowl.
It's sometimes the little things that kill you so double check all your soft line connections before condemning the fuel pump.
You could possibly have a problem related to the tank sealing process and material or a damaged pick up tube in the tank.
What kind of car and tank are we talking about? Older cars had the pick up tube coming out about half way up the side of the tank and the bottom laid right down on the bottom of the tank. They are non removable and some tank sealer could very well have ended up in it making a blockage.
Mike
