If it runs longer cold than hot, and if it coughs before it stops, seems like it is mixture not ignition. I'm not familiar with that carburetor but I have the impression there is a priming bulb which shoots fuel into the intake manifold when you pump it. Perhaps you could try pumping this when it is in the process of cutting out, to see if it comes back to life? That won't fix anything, it just confirms it is purely a fuel shortage that is causing the problem. Once we confirm that, I'll retire to the sidelines.
