I am experiencing this problem too, in exactly the way that you have described here. It has happened on a few occasions and on calls to different people. When I use my iPhone 5 on the same Wi-Fi network, it works as normal, so I believe this issue to be isolated to my Mac.
I would really appreciation an indication as to what might resolve this.
I also followed the link that you shared with nicholaslond. I went through the process of troubleshooting the FaceTime issue and it didn't resolve the original issue that I have with FaceTime (as per nicholaslond's description).
Do you have any other ideas about how to resolve this?