I don't know if Triumph decided to improve the wiring from my 05 model to the 09 model, but we would hope so. The wiring I'm talking about is what determines how much charge ends up from thre alternator (generator) to the battery.
In my case I broke down twice in 6 months because of a certain amount of load I was drawing with accessories and the poor charging capacity due to too much resistance. The resistance I'm referring to is twofold. One, the gauge or thickness of the wiring from the alternator through the regulator was too small and two, from the path between the Alternator to end at the battery was way to long. Hence the charge was too low if you were running anything more than a headlight.
It would be a good idea as has been suggested to check the amount of volts being delivered to your battery when above idle. I don't know if Triumph sorted out the wiring issues I just mentioned but if they haven't, I suggest you either check the voltage yourself (it really isn't hard) or get your dealer to do it for free (better idea) to ascertain if your battery is being charged with other accessories drawing power.
I'd suggest you originally get your dealer to check the charge to see what they do and if they find a dead batter and just replace it, then ask us again how to easilly fix the problem yourself as this issue has been discussed many times before, or again, put it in the hands of the dealer to sort it.
Good luck