J......,
Make sure the frame/engine combo has a good ground between them. I had a similar problem on my 93 kx125, tried the CDI, then the coil (from my 250,same part #) and the coil fixed the problem. I then ordered a new coil & thought the problem was fixed. Same problem persisted put 250 coil back on problem fixed!?!?!? A new coil does NOT come with the cap so removed from the old coil & installed. The resistor cap was opening when it warmed up & lost spark. The problem was getting progessively worse.
Remove the kill button wires, check for frame/engine ground, remove cap (coil wire straight to plug). We do not need to loose any hair over this as I have already done that.
I hope the info helps, keep us posted.
DoldGuy