Password protected pages are not working with domain mapped sites.
Upon entering the password and clicking submit you are redirected to the Admin dashboard if logged-in. If not logged-in you are redirected to the not_found page.
Tested with default 2012 theme and redirects still occurs for mapped domains.
Tested with a non-mapped domain and it works
Also I have "https" applied to the admin back-end upon the redirect "https" is added to the mapped domain.
This don't happen to non-mapped domains