Domain mapping is not checking to see if wp-admin is forced ssl or if the site is in ssl mode, and then making its referenced url be in ssl mode.
As a result there is no domain heath check status coming through and in the browser console there is the error explaining why:
https://networkdomain.com/blogname/wp-admin/tools.php?page=domainmapping was not allowed to display insecure content from http://networkdomain.com/blogname/wp-admin/admin-ajax.php?action=domainmapping_check_health&nonce=87BLAHBLAH&domain=mappedomain.com.
Using nginx on my server.
Please forward this bug to the developer for review, would like his thoughts.