Ultimately it was necessary to restore through iTunes and set up as a new phone. It is inconvenient but it is the only thing that worked with one of two iPhones that had the rapid battery drain issue. We have 2 iPhones and 2 iPads. Each were updated with iOS 8.0, 8.0.2, and 8.1 in succession. Each without issues until the battery drain problems with the two iPhones. One responded with a hard reset. The other required the aforementioned restore and set up as a new phone. I took a step-by-step approach and attempted to trouble shoot as a non-technical expert starting with soft and hard resets. This high battery drain was clearly related to problems with the iOS 8.1 install and in one case needed a complete reinstall including selecting the set up as a new phone option to solve it.
My recommendation is to try the following steps in order of least troublesome to most troublesome: soft reset, hard reset, and backup and restore as a new iPhone.
1. Soft reset - Go to Settings ->General -> Reset -> Reset All Settings enter pass code. This resets setting without removing any data or photos from your iPhone.
2. Hard Reset - Hold down the sleep/wake top button and the home button at the bottom of the screen at the same time until the screen shuts off.
3. Restore -
Plug iPhone into your computer with iTunes and to a backup to computer (or iCloud).
Turn off Find My iPhone – Settings -> iCloud -> Find my iPhone -> Off
Go to iTunes and select your device then Click Restore
Follow the prompts and the iPhone or iPad
Monitor the install, it may take a while. When it is complete you can try doing a restore from backup. I tried this and it did not work. I suggest skipping to set
up as a new iPhone. You can then sync your data and restore. It is a hassle to do it this way but with one phone this is the only thing that worked.
You can do a search for any of these type of solutions such as Wikihow: http://www.wikihow.com/Hard-Reset-an-iPhone
There are other searches that can be done to fine tune battery life.