I can only speculate until I know what kind of car you have, but I'd suggest replacing your fuel filter for starters. Yes, a filter can act clogged one minute and act OK the next, at least in my experience. And yes, Fuel pumps do act up before they go kaputt. I don't know if your car has a fuel pump relay (my dad's 560sel does, and this relay breaks way too often). That should get you started.

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'82 300TD
'77 6.9
'75 280S
'74 280
'87 Porsche 944 turbo