Sorry to hear of your problems. I would do a check on the stator and VR as other have mentioned. Here is a good bit of info to give you an idea of how to go about checking it out.
http://www.bigdogbiker.com/forums/how/24664-stator-check-out.html
Also seems like there is allot of people that immediately change out batteries and go through a few with no luck. Batteries can be hit and mis for sure, but before ruling or replacing a battery, always would take one na dhave it properly check by a Auto Parts store or Battery dealer, one that can do a proper load test and inner cell checks.
Some batteries are better than other, no question about that, how ever for the majority, a basic battery that is AGM and meet the requirement will do. I think many will be surprised at the number of people that have had years with no starting issue with the OEM battery. Simple 270 cca amp battery.
If you got some heavy mods or one that is older that may not have Comp Release, than a more specialised battery is for sure something you should consider.
Main thing is to keep them on a good tender and unless known for a fact that it is bad, to check everything else. I have had my BD for 7 years and have found that batteries last me an average of 3 years or so, right now I have a cheap WalAmrt Everlast battery that is 2 years old and last time I was home, started right up, put over 500 miles on it with no issues. May be lucky, but all the BD OEM had similar luck with.
Anyway check out the link and recommend that you do all the checks and go from there. It does sound like a charging issue.
Good luck and let us know how you make out.