Based on your previous output of chkconfig --list, sshd is enabled on runlevel 5 so that's not the issue; runlevel 5 is I believe standard convention for graphical logins like you seem to be using presently, which is fine.
Ignore the systemctl comment; that's the tool to configure services under the systemd init daemon. CentOS uses either SysV (5.x) or Upstart (6.x), and the chkconfig/runlevel style of service management applies here. These are just different processes for managing the system and its services; distributions like Arch, Fedora, OpenSuse, and possibly the next version of Debian use systemd by default, but that's besides the point.
I'm assuming you haven't yet discovered the problem causing your ssh issues? If not, the next step would be:
and see if it outputs anything; if so you have a misconfigured /etc/ssh/sshd_config and need to fix that followed by
Otherwise proceed with
grep 'sshd' /var/log/messages | less
grep 'sshd' /var/log/secure | less
and scan the latest entries for any trouble signs - warnings and the like. If you find anything and want to output it here you could run
grep 'sshd' /var/log/messages | tail -n 10
grep 'sshd' /var/log/secure | tail -n 10
or however many lines are necessary.