Sounds electrical rather than fuel related to me - fuel related tends to cause the engine to surge or falter before dying, whereas electrical faults cut out immediately. According to the Bosch manual, you need an oscilloscope to test the speed and reference mark sensors which are located on the bell housing between the engine and the firewall (as mentioned earlier), and very few of us have access to one...... I would suggest that you carefully check all the connections first of all, before you consider replacing parts - get hold of a copy of the 'troubleshooting DME' section of the workshop manual, and work your way through with a multimeter.
Does not sound like a fault with the DME relay, as I they pretty much just fail, and does not sound like ignition components as breaks in leads etc., normally cause cut-out one the engine has warmed, and will not restart until the engine has cooled sufficiently.
The engine/DME temperature sensor seems to be pretty critical on these cars as they seem to provide key data to the DME and failure of this can cause all manner of wierd problems. Couple of hours patient testing with a multimeter and a few jumper leads should help at least rule out the good components, and narrow the problem down.