That sounds very similar to a problem a friend of mine had with his finny. nobumps on here if you wanna talk to him about it, but from what I remember..
It could run mint for ages, a couple of hours even. All of a sudden it would stall and not start. If you waited for ages or tried push starting it would often start fine again and be fine from then on.
From memory I think it was rust and shit in the fuel tank. I assume that the fuel pump sucks up shit, then the car won't start untill it is turned of and the pressure stops, or until the blockage removes from the fuel line.
Hope that makes sense and things.