The only good advice I can give you, is to tell you that this is a common problem with Facetime for Mac. It happens occasionally to me also. But it doesn't happen often enough for me to get rid of Facetime for Mac.
The bad news, is that there is no viable solution. BTW Facetime, when used with an iOS device, such as an iPad or iPhone works much more reliably. This leads me to believe that there is some sort of incompatibility between the Facetime for Mac software and the Mac hardware.