Do you have a fuel pump gauge in line? How far are you closing the choke? I know more questions.
If the mechanical pump has gone bad they will sometimes suck most of the fuel out of the carb after sitting for a time. Electrics do not do have that probelm. Also if you are over choking the car at start up it will flood out and be a pain to start. Easy thing to check for flooding is black smoke out of the pipes at start up.
The AFB syle carb does not have a power valve that can leak down into the engine on shut down like the Holley so I am sure you do not have a carb leak problem.