vrs626:
look at your Settings > General > Usage
look at the "Time since last full charge"
Are the numbers exactly the same?
look at Settings > General > Diagnostics & Usage > DIagnostics & Usage Data
Do you have a crash in there that starts with awdd_2012 ?
I suspect there is a power manager crash for all of us.
I KNOW this is a brand new phone... something is wrong, but the fix appears to be brute force. Yes, as you said, the cause of the problem could be unrelated... but the solution appears to be the same.
You can either:
1. call apple/visit a genius (they will make you do all these steps)
2. try a full reset as described
3. return the phone and buy something else
PS -- I charged my phone when I got home from work today. My usage/standby numbers since 6pm:
Usage: 47 minutes
Standby: 5 hrs 28 mins
Battery remaining: 92%
I wasn't able to do this yesterday. It appears to be working after all the hoop jumping.