How can I keep iPad from logging out of iMessage?

How can I keep iMessage signed in on my iPad?

I'm not sure if this began when I upgraded my phone from a 4s to a 6 or when I updated the OS on my iPad to the most recent as those events happened on the same day. My iPad and iPhone used to coordinate messages well but no longer. I frequently find that the iPad has signed out of iMessage. I'm asked to enter my password and verify my email address, which is already verified. I need to restart my iPad, turn imessage off and on again and a few other apparently arbitrary things. If I'm lucky, it will work properly for a day or two and then I'm back to starting over again. Very frustrating!

I should clarify that, while I have cellular service, it is not turned on and I'm not sure whether I have an iPad 2 or 3.