The problem in my optinion are the scripts running care of Webmin/Virtualmin.
You have hardened the system so probably when the cron runs generates output of the failed shell commands.
Please take a closer look at /var/log/autdit.log for failed login attempts.
You caould also try installing "DenyHosts" is a perl daemon that checks for a number specified of failed ssh logins and puts automatically the attacker Ip address in /etc/hosts.deny.
We have install it on more that 16 servers and we actually have more that 160.000 ip addresses automatically blocked.
If you need further help i am here to assist you.
Regards