The Fuelpump starts work if the ECU notice a couple of RPM.
(afaik more than 50 but not sure)

Restart after the engine hast stopped is possible?

Maybee a bad grounding, wich looses connection throug vibration?

Gude Mario Audi 100 CD Autom. Bj.83 Audi 200 20v Bj.89 Audi 5000 Bj.85 Audi V8 3,6 Autom. Bj.88