Hi.I'm not really up on your particular model but i had a similar problem on a mk1 many years ago.
Do you have a mechanical fuel pump mounted on the engine or is it an electric one inside the tank like the gti's etc ?.
It does'nt really matter i guess but on the MK1 it turned out that the gauze filter on the pick up pipe in the tank was blocked (commonly called the strainer).
I put a transparent in line fuel filter into the pipe after the mechanical fuel pump and soon found that when it died i could see the filter had no fuel in it.It took ages to restart as you had to wait for the sediment that had blocked the strainer to drop off again until the next time.
Sounds very possible to me
