According to ComputerWorld its an Apple bug related to Exchange calendar use. See http://www.computerworld.com/s/article/9236792/Apple_takes_blame_for_iOS_6.1_Exc hange_battery_draining_bug_promises_patch
The workaround it claims is to remove your exchange calendar and then re-enable it. I gather from another posting that a 6.1.2 is due within a week but we'll see.
Quality problems like this drive users to consider alternative platforms. I left Windows Mobile for quality, Windows Phone for lack of apps, Android for quality and poor vendor support, and reluctantly picked up iOS. My experience has generally been positive but Apple doesn't have my loyalty; I am willing to try the other platforms again if Apple cannot get their service packs correct.