I just recently got a 1929 Model A. It starts fine
It sounds to me like you have a fuel problem. The first thing to check is your gas cap. The gas and radiator caps are identical except the gas cap is vented. Make sure your gas cap has vent holes in it. If that checks out OK, shut your gas off and remove the fuel line from the carburetor end. Put a can or jug under the gas line and turn the gas on: You should get a good constant flow of fuel. If not, check your fuel line and see what is holding the gas back. You may also have a plugged sediment bowl. If you are getting a good steady flow of fuel, check the strainer of the carburetor if you are using a Zenith carb. Sometimes there is too much fuel line sticking out past the ferrol. This causes the line to jam against the strainer screen and if sediment or something builds up there it will restrict the flow.