Stealth monitor of Security

I have a RedHat/Apache platform that seems secure but when I read the log files I can see it is getting hit at a very high rate by attempted illegal logins. Illegal email access attempts including trying to access a majordomo that I am not running.

Is there any stealth software out there that I can install to monitor who has logged in and what they did even if they erase themselves from the log files? It would need to be hidden so of someone does break in they would not know they are being monitored. I have a very low traffic site. www.evnsong.com is one of the hosted sites.
This is a web server platform and I am the only one with shell access. FTP is permitted but passworded.

Seems to be what I am looking for is some sort of virtual key logger that is hidden. Reading the log files is just not getting me the nice warm fuzzy feeling I want that my system has not been broken into.