I recently got my iPod Touch, and a couple days ago, I was signed out of FaceTime and iMessage (not by my own doing) and I haven't been able to log back in. I have already tried changing my DNS to 184.108.40.206 and 220.127.116.11, 18.104.22.168, I have logged in and out of my Apple ID on my iPod Touch, I have changed my email address and then changed it back, and I have used a different WiFi connection. The message that pops up (after it fails to log in) says, 'FaceTime Activation Could not sign in. Please check your network connection and try again.' This happens for iMessage, as well. I am using the right password and email, and I do not use an iCloud account. What should I do to be able to log in again and keep my email the same?
By chance do you have a cover/case on you iPod? Go into the room where your wi-fi router is and try again. If you do have a cover on it, remove it first to activate it and then if it works you should be able to place the cover back on still use it. I have a Survivor case on mine and that was blocking the signal needed to activate. It didn't get in the way of itunes, internet connection, or anything else. But for some reason it did for FaceTime and iMessages. Good luck!