Yea im saying pump issue.
Mine used to do this for ages, till some bright spark from RAC wired my Fuel pump relay so it was Live permenantly, it then used to suffer from a dead battery all the time.
New relay resolved the issue tho, along with ripping out the dodgy wiring job the RAC guy had done.
Check that power is running to the pump when its cut out! it should prime before you start the car (lift the back seats and put your hand over the pump or listen for this)