Since 10.11.1 Mail spends most of the time unable to connect to servers
Solution 1:
Check to see if you have _mbsetupuser
running. If you do your update to 10.11.1 (or to 10.11.2 or 10.11.3, for that matter) has not completed.
Though the "About This Mac" dialog may say that your version is 10.11.1, you are in fact effectively between versions, and will get all kinds of odd behavior (repeated requests to unlock the Keychain, connectivity problems, wifi issues, etc.) until you complete the installation process, which you should be able to accomplish with a reboot.
Solution 2:
I have also run into this issue after an update from 10.11.x to 10.12.
When SSH'ing into the server as admin I would actually be the _mbsetupuser account every other time.
Every other time I tried to connect via ARD I would be denied access.
A reboot did not fix the issue for me.
I had to create a new admin account in system preferences, log in as that admin, delete the old admin account, and recreate it.