Have the same problems here. I got it on 1st day. Didn't worry too much at first because I've noticed with my other iphones/ipads that it will take a few days or week (with several full charges) to get the battery life up and once it does it lasts as long or longer than they claim.
Unfortunately that is not the case with the 4S. If I don't put on charger throughout the day it will be dead within 5-6hrs with not a lot of usage. 2-3 if I try to use it regularly.
I'm getting about half or less battery life than I got with my iphone 4. Heck, I have to put on charger when I go to sleep or it will be dead by morning if it wasn't 50% or better when I went to bed.
I have the exact same config I was using from Iphone4... let itunes handle backup and restore. Only difference is iCloud instead of using Google apps to sync my data. Don't use iCloud for backup, but I understand that would only work if plugged in anyway.
Carrier is AT&T and I do live in an area that has HSPA+, I live just below San Antonio, TX (wihich has full 4G LTE).
I would return this but I've already sent my 4 off to my son in Nevada.