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Probably you have a XML-RPC attack toward your wordpress. The most common visual cue of this would be an “Error connecting to database” message. The web console may also display “Out of Memory” errors.
Or if the above method is not working for you, you can install “Wordfence” plugin for protection. It’s pretty great. https://wordpress.org/plugins/wordfence/
I had a similar problem and was able to finally fix it.
Background
I tried a bunch of tutorials that recommended tuning my MySQL installation and Apache configuration with no luck.
Identifying the Problem
It turns out that my site was being subjected to a brute force attack that targeted the WordPress xmlrpc.php file. H/T @sierracircle.
In order to check for this, you should view your apache2 access logs and look for suspicious POST requests. In my case, I found a huge number of POST requests to the /xmlrpc.php file coming from the same IP address (about 2 or 3 requests per second).
cd /var/log/apache2/
cat access.log
Solution
In order to fix this, I banned the offending IP address via Iptables:
Ban IP the malicious IP address (replace example with whatever IP address you want to ban) :
iptables -A INPUT -s 46.166.139.20 -j DROP
To view blocked IP address:
iptables -L INPUT -v -n
Reference: http://www.cyberciti.biz/faq/linux-howto-check-ip-blocked-against-iptables/