Yep, you were right on with that one, mates. I had used a decent amount of electrical tape to try and hold the cheap wire connections together better, but it just didn't stand up to the Arizona heat.
I'm thinking of cutting the stock connections off, stripping the wires back a tad, and using nice automotive ones. Pretty easy modification and will probably hold up much, much better.
Glad that fixed you up, it was the only thing that made sense ;-}
You are on the right track considering replacing the stock wiring, I re-wire all my 2-stroke builds with a 16g shielded wire pair from the magneto all the way to the CDI.
Just cut the mag wires off and solder one end to the magneto lugs.
NOTE: I use the new Skyhawk mags with no white wire, ground is the bottom tab, there is no 3rd ground tab.
Also note the wire I use has a red and white wire not blue and black.
Red is hot, white is ground.
Then just tuck the wire up with the clutch cable all the way to the magneto.
Stagger your wire cuts at the CDI and solder the kill button wire in with the mag wires and it leaves enough space to not use any e-Tape anywhere.
Glue a cover cap on and your set, and you can even get fancy with a keylock switch in the CDI cover which basically just shorts the ignition like the kill button so it can't be started without the key.
Use epoxy to glue the cover on if you put a switch in so it can't be defeated.
One last tip...
Get yourself an NGK 5944 (BPR7HIX) Iridium spark plug, they are perfect for our hot summer temps and all I use.