Drupal tracks your entry and exit from sites and uses that information to create versions that can be rolled back to in case of error or technical issue.
If you use the same browser to go back and forth from one Drupal site to another Drupal site the system thinks you are signing out of one and signing into the other.
So, you will keep losing your initial log-in.
It is recommended that you use two different browsers if you need to go back and forth between sites.