If your Apache web server stops responding and serving content, while you see there is plenty of memory available and low CPU usage, this could be a symptom of Apache reaching the MaxClients limit.
If you look in the main Apache error log, you will probably find this error:
server reached MaxClients setting, consider raising the MaxClients setting
You need to increase the amount of clients Apache can server. This is done by changing the MaxClients setting in /etc/apache2/apache2.conf (Ubuntu) or /etc/httpd/conf/httpd.conf (Centos). Check other Apache configuration files in /etc/apache2/conf.d or /etc/httpd/conf.d that may contain extra MaxClients settings. Make sure you restart Apache after making the change.
Keep in mind as you increase this number, Apache will consume more memory. So start increasing the number moderately until you find the right value for the resources your VPS has. If you need more memory, you can upgrade to the next plan.