I am experiencing a similar problem.
I am in the UK, I have an iPhone 4S (32Gb) and iPad 3 (32Gb Wifi only) and Apple TV 3.
The Apple Remote app to connect devices to Apple TV etc only works with my iPhone, the iPad does not now connect. It was successfully working up until last week but strangely has suddenly stopped. I have confirmed that all my devices are successfully connected to my home wifi network and that i have access to the internet, I can connect to iTunes etc.
I have tried many things, removing the app and reinstalling it, restoring and resetting the iPad and Apple TV, all to no avail. I have also restarted my router, changed channels, again without success.
iTunes Match servers where undergoing an update over the past couple of days and album artwork, songs etc may have been missing for some users as I myself found, but would this cause my iPad to suddenly stop connecting to Apple TV via the Remote app.... Unlikely I think.
Any suggestions would be most welcome.
It may be.
After reading through various discussions is the Apple Support forums regarding similar issues an Apple Support Agent suggested to a user to email him various findings specific to that post. I have sent this chap an email myself detailing my issue, I will report back any reply I am given.
It may be inconclusive though as I haven't really used the correct channels to report a problem, that is to say a chargeable method of reporting an issue :-)
I have performed further checks and it seems that i do have some functionality.
Whilst the Apple Remote app on my iPad doesn't appear to connect to my Apple TV so that I can use gesture controls etc to navigate the menus and control Apple TV, I can in fact Airplay content such as BBC iPlayer, Youtube etc. from my iPad to Apple TV as well as mirror content like Safari..... It is just the Remote App gesture navigation which doesn't connect/work.