could be autochoke unit has failed, it should have an electric heater inside as well as coolant flow thru it. check you get 12v to the engine side of the autochoke heater plug when the engine is stone coldm, and that the choke side has continuity to the choke housing. make sure earth strap between carb and rocker cover is there too. if you dont get 12v to it check the thermoswitch in the coolant housing, i forget if its the red or the grey one. one is autochoke the other is inlet heater. also check you hear tyhe valves behind the carb click when the ignition is on, maybe have blowm carb electrics fuse.
this can also be caused by insufficient coolant flow thru the carb due to blocked oring in the inlet manifold, is the waxstat warming up with the coolant or is it just from radiant heat from engine? the carb itself should get very hot very fast after warm up, feel the side coolant hose and compare the temp of that to the carb. it should literally burn you after a short while!
have a read of my 2e2 faq as well, it covers pretty much everything that can go wrong on em
