Hey Guys,
I fixed the problem on my iPhone 4S. I had upgraded to 6.1.1 from 6.1 (but I don't think it's really related to 6.1.1) the main difference was that when i unlocked and setup my device for the first time right after the restore to 6.1.1 (prior to restoring from an itunes backup), I setup icloud instead of selecting "skip this step".
I had to go through the setup wizard because I "escaped from certain shackles". Not sure how many of you here do the same.
In anycase, Try going through the setup wizard on the device prior to restoring from a backup (either itunes or icloud), and make sure to go through the icloud setup (don't skip it!).
FYI, I also tried resetting network settings and that didn't help. I was also getting battery issues which prompted me to upgrade to 6.1.1. No battery issues anymore (even though I restored from a backup)