Here are some things you can look at, not in any order.

• When using an electric fuel pump be sure you have a regulator between the pump and the carburetor. Electric fuel pumps put out more pressure than your carburetor can handle. Set the regulator to 4 lbs.
• If you have a standard fuel pump test the pressure. New fuel pumps are especially suspect.
• Test the needle & seat. This is the most likely cause. Dirt may have gotten into the seat and happens more than you would think. Rebuild the carburetor, put it back on the car and crud from the gas tank gets into the carburetor. Fuel filters will not stop everything. Try blowing air into the inlet. That might dislodge any dirt that is in the needle and seat, or float valve.
• Test the float for leaks. Shake the float to see if there is fuel inside. If it has been sitting for months then the gas inside the float may have evaporated. Heat up a pan of water just prior to boiling and immerse the float. Any bubbles indicate a leak.
• Move the float up and down by hand to see if it is catching. It could be the float pin is worn.