You are not alone. I tried all the fixes, multiple times, but nothing worked.
I think there's nothing to do but wait. The fact that many of us are experiencing the same problem with the iPad Remote app, and the fact that the iPhone Remote app still works fine, tells me it's a glitch in the software - maybe Apple TV 5.2, maybe iOS 6.1 (I updated to both yesterday).
Meanwhile, since Apple does not read these forums, I suggest we all leave comments on their feedback page: http://www.apple.com/feedback/appletv.html
That way they'll at least know a bunch of us are having this issue.
Hopefully Apple will issue a fix soon.