How do you know at this point whether it's fuel or ignition?
For testing, go down to Radio Shack and get an NE-2 neon lamp. "Rig" the lamp up where you can see it, such as a slot on the cowl and some tape, etc, ground one lead. Run the other lead with some wire down and wrap 4-5 turns around the outside of the insulation of the coil wire. This should make the neon blink when the engine runs. It will quickly show you if the ignition is dying or not
Make a couple of tests. Put the key in "run" engine off. Check the "switch" side of the ballast, or if you don't know, try both sides. and pick the side with more voltage. Leave that meter probe on that ballast resistor terminal, and move the ground probe over to the battery POSITIVE post. You are hoping for a very LOW reading, the lower the better. More than .2--.3v (3 TENTHS of a volt) means you need to look at the harness and find the voltage drop.
Also "wiggle" the key in the switch and see if the voltage "goes away."
Next time the engine dies, do NOT crank it again. Pull the air filter, use a flashlight if necessary, and pump the throttle while looking down the carb throat, and see if you are getting fuel out of the accelerator pump.