User cannot manage DNS zone he owns.
Limit set for 'DNS Management' subresource was reached.
The limit of the resource 'DNS' defines how many DNS zones can be created in the subscription. That resource has a subresource named 'DNS Management' which shows how many of created DNS zones can be managed (enabled/disabled/edited/etc).
If limit for 'DNS' is set to 2, and 'DNS Management' is limited to 1, customer could have two DNS zones, but one of them will be unmanaged (the last created).
To resolve the issue, open the subscription's settings and increase the limit of 'DNS Management' subresource under 'Resources' tab.