As Wayne said could be an ecu issue although you need to rule the coil out completely..
When they start to break down they tend to short as they warm up and work when they cool down..
ECU relay is worth checking/changing too
Another thing to try is taping the key chip to the immobiliser pick up on the ignition barrel, as it may be losing its perspicacity

If you have a spare key with one try using that as well.
Either is Not a permanent fix but will get you going and a clue as to the exact origin of the fault.
Do not get distressed though is its easily fixable and not expensive

One of my Mk3's used to cut out after starting in the mornings, I used to bang the steering wheel fairly sharpish once and it would fire, did this for over a year
