I'm new to this discussion board, so bare with me. I own a iPhone 4s also. I too upgrade to iOS 5.1. I was one of the lucky ones that had no real battery issues. Well until I up graded to 5.1. My battery drained extremely fast and I really don't use mine intensely like others.
After hours of research and testi g on my own phone, I believe I have found the solution to the battery drain.
So far, after utilizing the steps I will outline below, my phone has held fast and stopped draining.
Here we go:
go to
SETTINGS,
GENERAL,
scroll to bottom and press RESET.
THAN PRESS ( and this is important) PRESS RESET ALL SETTINGS
( do not press ERASE ALL CONTENT and SETTINGS) !
Pressing RESET ALL SETTING will NOT delete or erase any apps, photos, videos ect.
What it will do is reset your phone back to FACTOR SETTINGS and treat your phone as a newly programmed phone.
You will NOT loose your cellular carriers connection either.
After you have pressed RESET ALL SETTINGS, the phone will cycle through it's resets ( ie. Switch off, display apple logo and progress bar, shut down again, show apple logo and another progress bar and than shut down. ( patiences is important here. It takes a few minutes)
After all this turn phone back on. If you had a custom background screen and lock screen, they will be gone but fear not. Go to SETTINGS, WALLPAPER and to your photos and change it back.
You will also have to enter in your custom settings again ie. Reenter password for WiFi and other custom changes you did to the phone originally.
NOW here's the last step after you have added back your custom changes: go to your physical home button at bottom of phone and DOUBLE CLICK to bring up short cut apps you use the most, HOLD down on one of the short cut apps to get them to wobble and show minus sign and DELETE every one of them. AGAIN...DELETE shortcut apps not actual app.
This function that keeps your most used apps available for instant access, actually drains your battery considerable. It actually keeps them active and not dormant.
Personally I think they need to get rid of that function.
My battery life held fast now. Usually at 100% it would have drained almost 30% or more over a short time but now it really hasn't moved.
Only pain is that you will have to remember to delete these shortcuts more often.
Good luck. Hope this helps