RSI (Europe) helpdesk here:
Eticket - do you have an electric fuel pump? Is it wired through an
oil pressure switch?
If so - check the wiring, could be the switch breaks on rising
oil pressure (i.e. as the engine starts), stops fuel pumping - engine stops. Then when you check your fuel pressure with the engine stopped - bingo! it's back.
Believe it or not, I have seen this before - the guy had tried 3 carbs, 2 distributors, several ignition packs, and was about to commit suicide. When I diagnosed it he was so annoyed he never spoke to me again. His loss.
HTH