Hi. I've been keeping a close eye on these forums since suffering form the dreaded 6.1.3 battery drainage issue and I think I've finally cracked it. I downloaded IOS 6.1.3 over the Easter Weekend and on returning to work found that my battery had drained to 20% within four hours of taking it off charge. Having researched various forums over the following week I became convinced that something in 6.1.3 had interacted with my iPhone 5 configuration to cause battery drain issues. In fact I don't believe the battery was draining fast at all, rather the OS thought it was and reported it as such before shutting down when it thought it had drained completely.
I tried restoring the phone before reinstating my Apps etc. from the back up. There was no improvement and I was forced to keep my phone on charge while driving to the office and during the day at my desk.
Yesterday I read a post where someone suggested restoring to factory default using iTunes but without restoring the backed up apps and data afterwards. Instead I set up the iPhone as a new device. The only other changes I made were to setup Outlook Exchange, Hotmail, Bluetooth and my home and work wireless network settings. The battery held its charge just like the good old days throughout yesterday evening. I powered down the phone and put it on charge last night then took it off charge with 100% at 06:30 this morning.
I drove to the office without charging the phone, and it's now been exactly five hours since it came off charge and the battery level is showing 89%. Up until yesterday my phone would have died by now.
My next step will be to reinstall the Apps gradually, one by one, direct from the App Store rather than from my last iTunes back up. Fingers crossed!!!!!