i have exactly the same problem. it drives me nuts cos i cant find out what it is. you'll find once it cuts out though if you bump start it and turn it off straight away then it will start fine again and again, mine doesn't seem to be the battery. i thought starter solenoid too. but i dont know. i recently redid all my earths and that made no difference.

if you find out what it is please please tell me what it is