The login authentication cookie is saved for separately each host name and domain name on a DNN install.
If you happen to have more than one host name . domain name combination pointing to the same portal and a user switches to a different one then they will be logged out.
This is by design. The concept of having more than one host name . domain name pointing at a DNN installation is usually to seperate the different portals within one DNN instance, so you can't login to one portal and get access to another.
This is right in line with my opinion about it not being good practice to use a shared SSL certificate for multiple portals or for multiple IIS websites.