If the apple Apple ID you have is set to use two factor authentication (as I do) its worth remembering that applications iMessage and facetime uses a unique app specific password - so just putting in your regular Apple ID password won't solve the problem
Go to manage Apple ID on the Web, login to My Apple ID and you can generate app specific passwords there for FaceTime and iMessage and use this password instead.
Get 
Sign up
Join
When your the Mac KEEPS ASKING for your icloud password