A few weeks ago I installed iOS 7.1 on my iPad 3 device. When using the iPad before, I could easily using it for over 10 hours on one battery load. After the update this was reverted to 3 a 4 hours max. This is called extreme battery drain! After upgrading my iPad to iOS 7.1, while in standby mode with cover closed, will drain from 100% to shutdown in under 4 hours! I did multiple actions to bring battery life back to default, but nothing seems to help. My actions were:
1) Soft restart the iPad, Using the Power button only
2) Double click the Home button and close all running apps
3) Change settings to disable "Background App Refresh" on all apps
4) Hard reset the iPad, using both Home and Power button
5) Bring back the iPad to factory default settings (using iTunes)
In my case option 5 (Bring back the iPad to factory default settings) was the only one which did the job. When using iTunes for that a full back-up must be created first (using This computer & Encrypt local backup). I did a sync off all apps also! Just install iOS 7.1 again (using Restore Files) and do a full restore after that (using Restore Backup). After that iOS 7.1 will be running fine again. Hope it helps!