I have a 2012 11" MacBook Air and I've experienced the same issue since owning it. By chance do you use an android phone? I have a Galaxy Nexus, and thus I have android file transfer installed for when I need to transfer files via MTP. Anyway, just like you said, the camera works fine until you sleep the computer for extended periods of time. After awaking the computer, just like you stated, I can no longer use the facetime camera in any of my apps. It says no camera detected.
Rebooting fixes this problem, until you sleep the computer. After poking around I figured out that, after waking the computer, if I go to activity monitor and find the "android file transfer agent" process and close it, the camera starts working again. I'm not sure why, but there seems to be an issue with that process running in the background after you sleep and/or leave your laptop running for extended periods of time. Hopefully this is the same case with you. If not keep us posted. I never had this problem with the 2010 Mbp that I had running Lion. I'm assuming it's an issue with the MacBook Air and/or Mountain Lion, but I could be wrong.