So reality is this:
Battery Tender: Will trickle charge the battery, if set properly and the only way to do this. Some people run straight charger and this will kill your battery as it wears down.
Running the bike on idle, wont do anything for winter use.
Some people will pull the battery out of the bike completely, and this is what I did when I lived out east. In perspective I always knew I would kill batteries it was just a part of it.
As for why you're battery won't power the bike, same check main electrical and kill.
1997-2014 United States Army A/R/SO JFK
Never forgotten, never forgive