Thank you very much for participating in this discussion and taking time to give advices.
Of course I agree that just because something seems like a bug , it doesn´t mean it really is. But as you can see from other threads, there are quite a lot of people describing this situation.
I have both an iPad2 and an iPhone4S running iOS8, so I will first try to install the just released updates.
But could you please explain what you mean by saying "there could be an authentication problem"?
I use iCloud a lot. On the web (iCloud.com), om my iMac, on my iPhone and on my iPad. I use iCloud for almost everything. Mail, calendars, contacts, Safari bookmarks, notes, reminders, find-my-every-iThing, Photostream and iCloud Drive for Keynote, Pages and Numbers. And I use iCloud for synchronization of different iPhone and iPad Apps. I have no issues at all with none of these. I have no problems with verification of my iCloud account with any of these services. And I also use iMessage and Facetime with the same account. I have no problem activating iCloud Keychain on any of my devices. iCloud Keychain is working all the time on my iMac. The only issue I have with iCloud, is that after one or two days, iCloud Keychain is turned OFF on my iPhone and/or on my iPad. How do you explain that with "an authentication problem"?