Mine runs the backup, which is only supposed to run when it's plugged in, although sometimes it seems to run through the battery faster for some reason.
I seem to get cycles where it lasts a week, or more, and other cycles where it seems to last less than a week. It's odd, and I was thinking about that just yesterday.
I do have the Logitech Harmony app, and it keeps the iPhone from sleeping, so it will smoke through the battery if I don't stop it and sleep my phone.
It's also set to auto-update apps, and sometimes, judging by the iMac updates, seems to have sleepless nights where it's updating a lot of apps.
I've had it loose 10% over a night, but I've also had it stay at 100% for two days.