The only starting problem I've had on my 80 was due to a small leak from the cold start device on the the fuel pump. I presume it was allowing air into the fuel system and was always worst after the vehicle had been stood for a while. Certainly worth a look
The engine should start without glow plugs as it is direct injection, but they help with emissions, the plugs are daisy chained with a common earth, take out five and one will still work.
I would go with a fuel leak from pump, or the diaphragm/filter head, very possible a slight leak letting air in and fuel running back to the tank, think of the finger on top of a straw full of milk principle.
A real shot in the dark (that is really dark), the fuel plunger may be sticking, or wiring leading to it being fatigued or corroded? Starting the engine lowers voltage to the solenoid, so insufficient power to lift the plunger, then the engine gets a good shake from giving it a 'sniff' and elevated voltage from the alternator once the engine is running keeping the engine going.