Checkmate! The server has rebooted and all the containers are DOWN.

Its easy to make the containers reboot automatically. Use a RestartPolicy

Edit the restart policy for an already running container:

$ docker update --restart=always container01

Check the changes:

$ docker inspect container01 | grep RestartPolicy -A 3
            "RestartPolicy": {
                "Name": "always",
                "MaximumRetryCount": 0

Your containers should now reboot automatically - but check the different policies, to see which one applies best to your case.