Same thing happened to me. Have had my 16bg 4S for about 4 days now (over the weekend) and no problems until this afternoon. Went to check/see if I missed any calls and it was unresponsive. I know I had about 80% + battery when I last talked on it (about 2 hours ago). Thought it was odd. Tried plugging in charger - no dice. Checked this site and seems I am not the only one with the problem.
I had a 3gs for 2 1/2 years and no problems. Kind of bummed that there is such a glitch right out of the box. I waited for a "new" version of the 4 before jumping over due to the problems plaguing the 4 when it came out.
I was using Siri right about the time this all happened...like the posts above, certainly may be connected. However, I have used it quite a bit the last several days and this is the first I've had any issue. Like a previous poster and I am sure, many of you, I cannot afford to "miss" calls and the thought of having to make sure my phone is on every 5 minutes kind of defeats the purpose of a mobile phone.
Have not tried any OS updates so far (if there are any). Will post as soon as I learn anything new.