Yep, sounds like a fuel delivery prob to me too. What shape is the gas tank in? The pickup screen in the tank may be getting plugged, and the sit time gives allows the vacuum in the suction side of the pump to drop.

Try inserting a fuel presure/vacuum gage on the intake side of the fuel pump and see if you are developing vacuum in the pickup line. Also you can use the same gage on the outlet of the fuel pump to verify the fuel pressure delivered to the carby.