Not logged in on Mapped Domain

I am sorry this seems to be a bit of a repeat, but the previous thread related to the problem was closed, and yet, I am experiencing it on the latest version of the plugin (4.1.2).

Basically, I have mapped a domain to a subdomain on my Wordpress Network. All seems to be fine with that part, and no issues accessing the Dashboard. The problem is that the admin of the site with the mapped domain appears to not be logged in when viewing their own site. No Admin bar at the top, and unable to do things one should be able to do in Wordpress when logged into their own site.

I believe I have tried every possible setting combination, but am willing to try more. Please advise how to solve the problem!

Thank you.