had this prob. myself ? change the realy first if that does not fix it you will need a new fuel pump my mk1 done this and eventually i traced it to the pump itself, allthough it can be a few things pressure reg fault can cause your pump to give up so can sh!t in the tank blocking it and the fuel reg , get under neath and take of a few fuel lines, the first one i took of was the one from the pump side to the reg to see if the reg was getting fuel and hey presto no fuel going to reg ,all electrical contacts were working pump was buzzing but not getting enough fuel thru and causing relay to click in and out , but like you mention for some reason when the car had warmed up a bit it seemed ok! :-[ :-[
regards kevin (best of luck)