Unfortunately, it's happening to quite a few of us.
There is no tried a true solution since none of us really know what caused ot or if it starts working again, why.
But here's somewhere to start.
The official answer If you get an error when trying to activate iMessage or FaceTime - Apple Support
The unofficial answer:
In order to get your time zone and time to update automatically, you need to have Location Services on. In iOS 8 it's under Settings, Privacy. Go to the bottom of the page where it says System Services, select that and make sure Setting Time Zone is on.
I suspect sometimes this still doesn't get the iPad to a time close enough to work, but it's a start.
Go somewhere to use another network, like the Apple Store. Try there. That way when you call Apple and tell them it's an AppleID problem they won't try to charge you.
Check out from page 18 on imessage and Facetime sign in activation error iPad ios8.1.2 and see that we've all been trying.
If none of this helps, call AppleCare and insist on going up the tech support ladder. Second line or Senior Tech is as far as they'll send you, those guys talk to the engineers. Keep trying.
I don't know if Apple really knows what's wrong either but this way they know you have a problem.
Keep us updated!