2006 triumph america cuts out, seems to lose power, run on 1 cylinder, have had 20,000 major service, carb serviced, tank checked (no debris). Cold, warm, or after rideing hard the problem can crop up

Usually when a problem like this only occurs when cold, it is a fouled spark plug. Check that first otherwise I would have the carb and possibly valve adjustment checked.

Buy a Yamaha.

You might try looking at your transistor it could be the cause of your problems. Even though it is a carb bike it will still have an transistor pack or similar that controls your spark. It is possible that failed. Try one from a bike that you know is working if that makes a difference that is your problem.
Although I'd also look for broken wires and poor contacts.
If your good with a multimeter and you know the specs of your coils and transistor than you can try and test them.

A good plan, but if the bike is already missing now and again, I would be tempted to strip and clean the carbs.
It would be worth cleaning the tank out as well.

make sue no movin parts are froze up or rusted-is cylinder and crankcase lubricated--try jumpin it from a car 1st--chec for rust in fuel lines and carb--clean all rust from external--ignition parts may be corroded-let me know

My friend, you leave a lot open on this question. You ask about 20,000 KM, is your bike sold for the USA market or another country. Service requirements are different for different countries and different for different kinds of service. Might this be a bike you bought overseas and imported to your present area? You don't say from whence you hail ... nor from whence the Triumph hails ...

It seems you are a devout Triumph owner/operator - spmeone who is intersted in maintaining his motorcycle at the highest level. With that in mind, I offer the following: it my suggestion is you to find a dealer in your area and ask them this question.

Better yet, since it is winter, take the bike to the shop, tell them you want it put in proper order and you will be back when it is done.

If you have more concerns, please post your comment to this question and I will respond.

Thanks for posting your question to FixYa.com

Just a very quick check,Swap the sparkplugs over.Don't put in new ones.If the problem follows that plug,it is only the sparkplug.Hope you get it fixed

I have a friend that has a 2006 Triumph America and the same thing happened to him. Started running on one cylinder and then just refused to start. I did a check on everything and found that the CDI went bad. This is mounted under the fuel tank along the back bone and is about 3 inch square box.
They mounted them with a type of plastic rivet and would vibrated on the mount and cause something inside to break. When you replace it mount it solid and use a piece of rubber between the mounting plate and the CDI.