Your IP is blacklisted in /usr/local/directadmin/data/admin/ip_blacklist. This is controlled by the "brute force login detection" in Admin Settings. Use a setting no lower than 10, since even loading the login page counts as 1 failed attempt.
Binaries for a different operating system. Related
You can always try running DirectAdmin by hand (if it's not already running) to see what the problem is.
to start it in the terminal with debug level 200. Use Ctrl-C to stop.
If DirectAdmin is running, is bound to port 2222, but doesn't respond on "127.0.0.1", but does respond on "::1", then it's an IPv6 issue. This guide would be related.