Hello People.
I've been having the same problems, namely the fast iPhone 5 battery drain after installing iOS 6.1.
I was having the same symptoms as all of you. After installing iOS 6.1 with 3G or Wifi on standby, my phone lasted about 12 hours, whereas before the update to 6.1 it was lasting me approximately 1 day and a half. While using it for about 2 hours a day between phone calls, mail checks, some game playing and app use, it started draining even further to a point to where the battery life was as at an average of 20% from its previous 100% after just 6 hours of use. I was having a day and a half of battery life in the previous iOS and was happy for it comparing to how things turned out to be...
So, i went to an Apple Store here in Portugal and they did me a diagnostic test to my iPhone 5. The phone passed in all tests except in the iOS version. It failed in Apple's own software test. Amazing...
Then, they recommended to me do a total restore to factory settings, which i did.
The phone got better...but it think that is in part due to my decision to test its battery life without any additional apps or resources installed. I've only imported my contacts from iCloud, and everything else is just factory settings. I've made a few phone calls, answered some sms's and used bluetooth on my car for about 10 minutes, but didnt use Wifi or 3G and turned off locations and push. After almost a day the phone is at 32%, but this is not surprising since i've barely pushed it and didnt use any apps with all internet access turned off. And it got to a point where in standby, i've noticed it starting heating a little bit in the middle of the day...
Another relevant point is that when i went to bed, the phone was at 88% after three hours on standby, then i've set the phone to flight mode and it only drained 1% in 8 hours. This was good, but after i turned flight mode off the draining started again...
Today i went back to the store with the phone totally restored, asked for another test and guess what? iOS still failed to pass Apple's own test.
It's clearly an iOS 6.1 problem.
And other thing, previously i've only used two Gmail accounts. I don't have an Exchange account, so by my experience, i can count the Exchange option out of this problem. I also had my email preferences set so i could access to it manually and not through push.
What i can say is that after restore it is indeed a little bit better. But i'm going to do another test tomorrow by restoring everything i had previously via iTunes. I'll tell you if the restore really did had an impact.
Apple's got to fix this quickly. It's my first iPhone and tough i like it, i am starting to get seriously disappointed because i need to be able to carry the phone with me to work throughout a whole day, without the worry of having to charge it two times in 24 hours...
Fix this Apple!