Hey insider50 , I just went on a 1000 mile ride on my 03 speedy, me and the bike were becoming 1, untill the ride home. I was going 80 on the interstate it was losing one cylinder, I pulled over and without stalling , ran good again, I went about 20 miles and it did it again. this happened about 2 more times and the last time both cylinders quit. i pulled over and it would not start. I could hear the battery start to die, so I waited about 2 min. and tried again, it started right up like nothing was ever wrong! . I made it home and was poking around the internet and found this forum entry:http://www.triumphrat.net/cruisers-america-speedmaster/111848-speedmaster-cdi-problem-2.html
Long story short , I bit the bullet and bought a CDI from a Triumph dealer. Surprise this gadget was back-ordered, Later I got a call they just got 4 in the country from the UK, I grabbed one. I could have let them check it out but I was afraid to spend a lot of time and money and the problem not happen for them. I did check all my connections first though, and the correct spark plugs were being used. I just got the bike last dec. only had 2500 miles on it. Anyway I had it out last Sat for 120 mile test ride , no problems. BTW the cdi is 589 bucks US. Hope this is not your problem , but just thought I would share the info...
good luck!