Hmmmmm- - - - - -
Try a little diagnosis at the next cold start. Pull the air cleaner, and see if the accelerator pump is squirting any fuel into the carb venturi before you crank it. If not, pull the fuel line, and crank for 10 seconds or so with the line going into a catch bottle. This will tell you if you're dealing with a dry carb, or a fuel pump that's losing its prime.
A fuel pump has one-way check valves that should prevent the gas from draining back toward the gas tank. If you crank it against a vacuum gauge attached to the inlet line, it should pull about 10" of vacuum, and hold it for some time (maybe 15 seconds) after the pump stops operating. Ditto on the outlet side, up to 3 or 4 pounds of pressure, and this should also hold for a while. If either vacuum or pressure is low, or won't hold its value for a while, trash the pump! Also check for air leaks or restrictions between the tank and the fuel pump. Pinhole air leaks on the inlet side are bad about letting a pump lose its prime, without making any puddles!
Jerry