When I collected my 1.6 Vx from its previous owner, I got about an hour into the journey home and it cut out.
I'd sit for 10 minutes or so and it would restart, only for the same to happen another 10 minutes down the road.
I thought it could be a blockage in the carbs, and so removed them, ultrasonically cleaned them and rebuilt with new gaskets etc.
Only for the same thing to happen about an hour after taking it out again. This time though, I was pulled over on a quiet country road with no other noise around and could hear the unmistakable sound of air leaking from behind me.
I twigged it was a vaccuum being created in the fuel tank and the fix was drilling a small hole in the fuel filler cap underneath the catch.
The previous owner had replaced the fuel filler cap after losing the previous one, but it wasn't vented and neither was the tank.
Your issue may be completely different, but at least this is an easy one to check.