Battery problems. Very, very frustrated.

[Midian]

Hi all. Picked up my fiancee's 2001 GZ less than a year ago for a song. It needed a new battery when we got it. I went and ordered one from Advance to the tune of about $100. They put the acid in, threw it on the charger for about 20 minutes, and sent me on my way. I put it on the bike and it started fine, but a couple days later the battery was toast because it wasn't fully charged the first time around. I exchanged it for another battery, bought a charger, put the acid in myself and charged it fully. No problems since. It got unseasonably cold here in January/February and we (stupidly) let the bike sit for a while. Sure enough, when she went to start it again, nothing. We jumped it off from her car with the engine off and it started up just fine. She rode it to work and when she tried to ride home, it wouldn't start again. I came up and jumped it off again with my car (engine not running, once again). The bike started fine. She rode home, and sure enough as soon as she turned it off it wouldn't start again.

I pulled out the battery charger and hooked it up to the bike (battery still installed on the bike, charger says this is okay). The charger claims the battery is "charged," but the bike won't even try to turn over. If you turn the ignition to the ON position with the charger hooked up, the headlight comes on and the charger says "charging." It will remain "charging" this way for about 10-15 minutes, then the headlight goes out and the charger says "check battery." If you turn the ignition back to OFF the charger once again says "charged." The bike will not even attempt to start.

Nothing was drawing power on the bike when it was left to sit and nothing is drawing power now. The ignition has been in the "off" position the whole time. We installed some LED lights on the bike but made sure to put in a toggle switch so they wouldn't draw power unless we wanted them to. I'm aware, obviously, that a car left to sit for a period of time will often end up with the battery discharged, but it's usually a simple fix to jump it and let it run to recharge. I also realize that the GZ engine probably doesn't have the power to recharge a battery by running it the way a car would, but shouldn't the battery charger take care of that problem?

Has anyone encountered this before or does anyone have any suggestions? My fiancee is starting to get pretty irritated with the bike and I'm not too far off myself. Is this battery no good? Do I really need to spend $100 on a battery for the second time in a year? Will it help to pull the battery off the bike and charge it, or will I just get the same result?

I hope there is a simple solution to this. This is our first experience in owning a bike and this battery stuff has been a real pain. If it comes down to having to buy another battery this soon, I think she might rather just try to sell it for what we paid for it and call it a loss. Are all motorcycle batteries this fickle or is this specifically a GZ (or small bike) problem? Thanks for any help anyone can give.