From my experience, this might be due to bug in 5.6 version of os/kernel.

We had a similar report from one of our customers.

Try to roll it back or upgrade to other OS.

If you did not find any thing from /var/log/messages

check cron jobs by "crontb -l"

I did all the steps. but when i use /etc/init.d/syslogd restart or syslogd service start it's saying now syslogd.

Please help me to install it on centos 5.6 x86_64.

You can see /var/log/messages or

vi /etc/syslog.conf and add this line

*.* /var/log/messages-new

and save

touch /var/log/messages-new

/etc/init.d/syslogd restart

When you say it shuts down services do you mean they crash ?

What does /var/log/syslog say when it happens ?

Could it be Apache is too busy and fails or there's bad Wordpress code executed causing it to fail ?