You may have a broken wire in the harness. It's a pain in the butt but you need to check for continuity in all of the wires between the CDI, stator, coil and kill switch. Start with the kill switch because it can short out too. All of the wires are color coded so just work your way through them systematically until you find an open. Also, jiggle the harness when doing it to catch any intermittent opens.
The cdi is probably the component least apt to cause you a problem. I would start out by taking an ohm meter and checking all of the components and connections before spending money on parts that aren't bad. BTW look at the kill switch, the stator assembly, ignition coil etc....