You can try to combat it by properly tuning your timing and your carb(and/or just idle screws). Often times you will find that one is out of whack and someone dialed up the other to compensate.
I think I had a similar issue not to long ago when doing my T-5 swap. Is it just turning over some more after you turn it off? That's deiseling and from my experience is usually a timing issue. Is it actually cutting off and then trying to start back up? If that's the case try and change your ignition switch, it's easy to do, takes 10 minutes.
On older engines this can be caused by carbon build-up in the cylinders. It raises the compression and holds heat in which will cause deiseling. Poor timing and low octane gas can also contribute to the problem. I had this problem on my 68 until I started using premium fuel.
It would turn over about twice then seemingly die then sputter back up a few more times after seemingly dying. Set the timing down a little on it and it seemed to help but I think its the carb mostly. Put a different one and it needs some tuning...abit lean for one...gap down on it and it just bogs and dies.