Do the following:

1. Upgrade the kernel. The one you are running is slow, has bugs and has security vulnerabilities

2. Make sure you are an up to date compilation of httpd and php (i.e. rebuild it through WHM).

3. Check in WHM > Apache Status to see what the children hogging resources are doing

4. When the server is under load, run the following to see if you’re getting DOSed from a single IP address:

netstat -autpn | grep :80

If you are, install an iptables firewall (e.g. APF wth anti-dos enabled and BFD installed) and block it. This would be a good idea anyway.

5. Install mod_dosevasive and mod_security

Also Modify the following to a reasonable value in Whm

WHM > Security > Modify Apache Memory Usage