Morning all.
So, I had exactly the same problems last week.
The issue, for me, was using quotas on shared iPad ADE profile. I had this initially:
(I originally had 5 as my quota size!). Anyway, using the above ADE profile resulted in the iPad logging out after a few seconds (with the "could not connect to iCloud" message appearing on the screen
Removing the quotas:
Resolved the issue.
Let me know if any of you have been affected by this and I'll check with Engineering