I just bought a new Mac Mini (2.6 GHz i7 CPU and 8 GB RAM) running Mountain Lion to replace my old decrepit 1.83 GHz Mac Mini with 3 GB RAM and Lion. I have exactly the same problem with maintaining the ability to sync my three iOS devices over Wifi. My system is 100% Apple: Airport Extreme Simultaneous Dual Band and Airport Express to extend the network (connected together with Gigabit wired Ethernet), the latest Mac Mini, iPhone 5 with 32 GB RAM, iPad 2 with 32 GB RAM, iPad Mini with 32 GB RAM. Both iPads have AT&T Cellular data and the iPhones are also AT&T.
All devices are connected to their respective power adaptors and are operating on the local WiFi (802.11n) network. I can get WiFi sync to work for a short time and within less than a day, it generally stops working (either the iOS device when "...looking for Mac Mini..." or the Mac when "...looking for iPad..."), sync never starts because the wireless devices can 'see' the network, the internet, iCloud, but they cannot 'see' the computer with which they need to sync.
This thread has been open since Sep 19, 2012, which is over 6 months! I never had a problem with WiFi sync when I had iOS 5, but it's been a constant problem with iOS 6, despite my replacing my iPhone 4S with iPhone 5, adding an iPad Mini and upgrading my Mac Mini essentially to the top of its line a few weeks ago.
This isn't a "Genius Bar" kind of problem since all of the devices perform well on both the AT&T network and WiFi, with the only exception being WiFi sync with iTunes on my Mac Mini. The iPhone 5, iPad Mini, and Mac Mini are all well within the 90 day phone support window, so the problems should be covered, however, the prognosis is rather dismal, based upon the almost 450 replies to this thread over the past 6+ months!
If Apple have weighed in on this, a knowledge item/fix would be appreciated. If Apple are not involved, then why not? Is the problem even acknowledged? I'm pretty much 'all in' with Apple. I also have a MacBook Pro for personal use and another MacBook Pro for work. Anyone? Apple? Buehler?