I understand your frustration. Having 'upgraded' my Mothers iPad2 to IOS6 some months ago, and my iPad3 to IOS6 at the same time, Facetime became unusable. For many months before this, Facetime worked flawlessly.
I spent many hours trying to fix this, but as I am in Canada and my mother is in the UK, elderly and not good with computers, this was really tough.
In the end we got it working, and the solution for was to have her service provider replace her wireless router with a newer model. This rather desperate measure was taken after I had read (In beleive in this thread) of some users having success after replacing their older routers with more recent models.
Even after we got everything working, we recorded upload speeds half that which could be obtained using a Windows 7 laptop, so I still suspect that wifi on these iPads are still not as good as they could be. Maybe Apple will work on improving this for their next IOS release. If you search this thread you will find my earlier postings where I provide the wifi test results (mothers iPad 2, brother-in-law's iPad3 and his Windows 7 laptop)
Although I don't seem to have a problem with Facetime on my end, I decided to read up on my router (a Netgear R6300) and was surprised to find that on the support page for my router, the first article listed under 'General Information' was titled 'wifi issues with IOS6'..
http://kb.netgear.com/app/answers/detail/a_id/21865
As I mentioned, my router is working fine with Facetime but it is interesting that Netgear have acknowledged there are issues. It is not only Netgear equipment which is having issues with IOS6 devices however. My mother’s router was a Thompson device. I read somewhere that someone believed that Apple was not following the wireless standard 100%. Perhaps they are using a mode which was only in draft when it came out, and is now supported in newer routers, but not the older ones. I don’t know if this is the case, but often wifi routers are released when the standards are in draft (my R6300 and my Dlink DIR-825 before that are cases in point). There is always a risk then that when the standard gets ratified, some draft feature is dropped or modified in some way.
I agree with others in this discussion, that there are multiple issues contributing the poor/unusable Facetime experience. Poor wifi is likely only one of them.
I am not suggesting you go out and spend hard cash to replace your router, but if you happen to have been planning on upgrading anyway, it might be worth bringing those plans forward. If your service provider supplied your router, then maybe like my mother, you can get them to upgrade it,
Good luck