Really easy way to confirm - pull the cover off the relay and make sure the contacts are clean and closing properly. Mine were not and you could tell the relay had been overheating for a while.

 

I may be talking rubbish but that won't be a first!, my mates 83 S2 wouldn't start 2 minutes after I started mine with a shake of a key after 6 months off the road, priceless- he swapped over his fuel pump with a spare and replaced the fuel filter (new) and was stunned by the condition of the fuel - a dark brown, from the filter, petrol goes through the pump first then the filter which, Mr Porsche I find a tad strange! He is convinced it had more to to with the filter- although he hasn't had a good at the old pump.

 

I don't know if it's been mentioned already.. but check that the fuel pump relay socket is making a good connection on all of the relay's spade terminals. A couple of years ago i was having problems with my fuel pump and I went through all of the run-of-the-mill troubleshooting for the fuel pump only to finally find the auxilliary contact (87) was loose where it makes contact with the socket. The multimeter was reading 12vdc on the backside of the relay socket (pin 87) but wouldn't carry the current required to run the pump. Always remember- if a voltage excites your meter it does not mean that the same voltage will support a load.

 

Conclusion:.... I replaced the fuel injection relay and the problem went away. I have been driving the car for weeks now with no recurrance of the issue. I disassembled the relay and it was not visibly bad. The contacts were free and looked great. The windings seemed fine. I didn't put power to it to test it but it was somehow bad.