You need to determine if you are loosing spark when the bike dies. The spark comes from: The sensor in the electric side of the bike then goes to the harness (check all the connections and be sure they are greased) then it goes into the CDI box, out of the box into the two wires on each coil, then to the spark plug.
If it is no spark condition, I would first check all the wiring by starting at the sensor wires (check for pinched/shorts), then progress to the coils following the path above. Take every plug apart and apply dielectric grease to them. You can also put a very thin film ont eh CDI connection, but it usually is sealed better than all the rest of the connections.
You said the dealer will let you try another CDI box, but charging you $50 to do so, sounds like an easy quick test to see if this is the problem. You can swap the box out in about 5 minutes too. Pull seat, console, tank and there are two small 8mm bolts holding the box in place. Swap and replace tank and seat. You should know right away if this is the culprit from your description of the problem.
You could also get one of the spark testers talked about in previous discussions, sorry don't remember who mentioned them, but you can connect it and ride the bike and look at them to see if the spark goes away while riding. Cheaper than the $50 to the dealer.
I would still try the gas cap too before this though. Can you loosen the cap when it starts to die and will it fire up again?
When it dies, does it do it suddenly, or slowly cut out and die?
When it stutters, can you crack the throttle open and make ANY difference?
What work have you done recently to the bike?
Checked the plug wires for nice and snug at both ends? Wires seated good in the caps? (they are not the best quality wires) Maybe the dealer will let you try some new plug wires first?
Bring it to my house and I'll figure it out in less than an hour. Bring cold beer. (yea, I know, you're far far away)
Any other members near you?
