I just now started getting this issue. I'll be honest I haven't tried anything other than the restore.
It started when I tried taking a pic of my friend at a concert and it just rebooted every time I tried taking a pic or video. Thought my hdd was full (only 8gig so not hard to do). So I deleted photos, music and apps and for a while it was ok made sure I kept about 1gig free. Note: up until this point i haven't had any issues with hdd space possibly causing issues or battery. And I always thought for the amount of use my phone goes through the battery life was good, AND STILL IS.
A couple of day's went by without issue. Then, out of the blue again it started rebooting almost every time I get a text message or phone call. That is the only time it restarts. Before I go buy a new battery and go through the problems of changing it I wanted to make sure the community (since apple is apparently mute on the subject) thought it was still a battery issue. Note: It also does it even when plugged into a computer or the wall.
Again, I only get the issue on incoming texts and calls. I can make calls and texts just fine.
I really wanted the 4s but if this is a precursor of how it's going to be count me out, I'll learn to love a Droid, iPhone is only apple product I own anyway. As long as I can make the phone a hotspot for my work I don't care I just want a working phone again.
Additional info: the issue started on 5.1 update and has continued over to the 5.1.1 update, if anything with the latest update getting more frequent.
Thanks in advance for the help all you guys are awesome!