I'm going to go out on a limb and guess that it's the battery. I say that because something similar happened to me. A relatively new battery (14mo old) would become useless even after sitting a week or two even with a battery tender on it.
After doing some research into "battery sulphation" back in 2002 I determined the battery I bought must have sat on the shelf for a long time. What happens to cause this is beyond the scope of this thread but the battery turned just fine initially after purchase. Over time it seemed to lose it's ability to pull high amps. Eventually even with plenty of charge time it turned the starter with difficulty. It measured a good 13.7v after charging but.... diminished capacity. Read more if you want at:
http://rollsbatteryne.com/docs/A%20S...%20Battery.pdf
You can also use a device to try and recover a sulphated battery. This is an example.
http://batteryminders.com/battery-sulfation.php
Given enough sulphation the internal current leakage of the battery is higher than the float charger...... the battery drains itself.
If it is the battery and you go for a replacement try to find a car parts or Walmart that has just opened. Chances are they have fresh batteries. Alternatively find a place with high turnover in batteries.
I hope I'm right on this. It's certainly going to be easier to replace the battery than to chase down something draining juice.
Good luck.