daperezg:

I was booting from SD when my problem started. What I finally figured out was that my other SD card got corrupted some how, which caused some error process to continually run, and that was draining the battery. (I forget where I found the details about this kind of problem.)

After I reformatting the corrupt SD card, the problem went away.

I'm usually pretty good at troubleshooting these things, but this time I jumped the gun, assumed the worse, and bought a new battery.