Server CPU usage spiking as soon as it's started

I use AWS EC2 servers for my web hosting and recently had a problem where one of my servers kept peaking out as soon as it was loaded. After moving the WordPress instance to another server and eliminating the possiblity that the problem was caused by the theme or Linux version I found the issue.

My server was being continuously accessed from a single IP source. I discovered this by checking the access logs like this:

tail -n 100 var/log/httpd/access_log

Source: http://stackoverflow.com/questions/12546858/where-do-i-find-my-amazon-ec2-access-logs

I could then see the ip trying to access the site every few seconds:

Logs

So the next step was just to block the IP address:

sudo iptables -I INPUT -s 191.96.249.80 -j DROP

sudo service iptables save

Source: http://unix.stackexchange.com/questions/32781/how-can-i-block-a-range-of-ip-addresses-with-an-amazon-ec2-instance, https://www.digitalocean.com/community/tutorials/how-to-list-and-delete-iptables-firewall-rules

Now the website is back to smooth sailing!

I was a bit disappointed with AWS support on this occasion. They weren't able to help me determine the issue aside from the fact that it was caused by memory use.

Hope this helps if anyone got the same problem.

Update

You may want to block an entire subnet:
sudo iptables -A INPUT -s 191.96.249.0/24 -j DROP

Source: http://www.linuxquestions.org/questions/linux-security-4/block-whole-ip-range-with-iptables-469432/

Or list your current rules:
sudo iptables -S

Source: https://www.digitalocean.com/community/tutorials/how-to-list-and-delete-iptables-firewall-rules