Since you say that you have had the carb. rebuilt, I'm guessing that it is not a fuel problem.
It sounds like you may have an electrical fault in the ignition primary circuit.
[sounds like your secondary/high tension side has been rebuilt]
Have a good look at the wires going to/from your ballast resistor and even the resistor itself.
Wriggle everthing while the engine is idling and see if there is a miss/cutout.
Can you describe what happens when it goes wrong, engine dead, still running, no guts or what?
Aways difficult to diagnose from a distance, but ....