I have an old iTouch with version 5.1.1. I am trying to set up iMessage with my daughter's Apple ID (not a child Apple ID account) and every time it tries to verify it brings me back to the log in screen. If I log in with my Apple ID or my son's Apple ID it works fine. So what is wrong with her Apple ID?
iPod touch, iOS 5.1.1
There's a problem with some AppleIDs and iMessage and FaceTime.
Most of us with the problem are using iPads though. When mine didn't work on my iPad my ID didn't work on an iPod Touch either.
Call AppleCare.
As far as I know it's some kind of problem at Apple's side. Don't let them tell you it's a network or device problem - tell them it's an AppleID problem so they don't tell you you are out of warranty - her ID won't work on a new one either. Tell them your ID works on it but hers doesn't and take it to another network so you can say you did. It took a month but mine is working now. I don't know what they did though.
One thing you can try is making sure the time zone and time are correct. That's helped some people.
Check outimessage and Facetime sign in activation error iPad ios8.1.2 starting at page 18 to see what people are trying
Good Luck!
Issue with specific Apple ID logging into iMessage
