WHAT could this be?!?

Well if it normally runs good then it could only be fuel or fire?? I would carry a small 12V test light so that when it dies you can immediately check for current at the coil, ballast resistor, starter solenoid, distributor or anywhere else there should be power when the key is on. If something is failing you'll either have to let it fail or find a way to isolate it when it happens. At least you can eliminate a few things with a 12V test light.
Fuel - if you have a in-line fuel filter right before the carburetor you can check to see if it's full of fuel when the car won't start?? But you're saying it won't turn over so that narrows it down to "fire".

treblig