To me it seems like there are two kinds of network hardware used in the AppleTV probably depending on when it has been manufactured.
For some people on this thread, the network completely stopped working with version 5.1 and the only solution was to revert back to version 5.0.2. For some of them, it seems like version 5.1.1 fixed the problem so all good for those. This is actually my case with my Apple TV 3 that was broken with 5.1 but now works well with 5.1.1.
But for those people like you who actually upgraded to version 5.1 without any issue, it seems that upgrading to version 5.1.1 might cause the network to stop working.
It's probably caused by something different in the networking hardware that need to be handled differently by the software so it makes it unstable. In other words, it's a major bug caused by faulty quality assurance and that affect both 5.1 and 5.1.1 versions!
It's very surprising from Apple that is actually producing it's own hardware especially to avoid that kind of trouble with the need to support differents hardware for a specific model. It's a little bit like Apple is not Apple anymore.
We definitely need a 5.1.2 version. And actually, the stable version is 5.0.2, should we understand that Apple need two iterations to deliver a bug free one? It reminds me another great software Maker :-)!