OK, I had the same problem with my iPhone 4s not recording audio when I would record a video.
It just started happening a couple of weeks ago. I checked all my settings and could find no reason for this. Then I thought back to about two weeks ago and remembered that is when I had UConnect installed in my '08 Jeep. It's a program for hands-free talking on the phone in my vehicle. To enable it, you have to have your iPhone bluetooth setting "ON". So I just turned it on and kept it on all the time. I was all set to make an appointment at my local Apple store when I remembered this and decided to check it out. It seems that that was the problem.
When I turned bluetooth "OFF" in my phone settings the video recorded audio normally! So try checking your bluetooth setting. Maybe that is your problem too.
