Fix Found: YES
Fix Complexity: EASY
Bug Description
The Apache http service randomly stops, this is usually after doing something in EHCP force web based control panel, that makes a change to the Apache configuration.
Symptom
You cannot see any of your websites in a browser, furthermore you cannot even see the EHCP web based control panel.
This is usually caused by Ubuntu server automatic updates.
The Fix
Connect to you server using PuTTY and issue this command to start the Apache service again.
sudo service apache2 start
Next, issue this command in PuTTY, to turn Ubuntu automatic updates off.
sudo sed -i "s/Unattended-Upgrade \"1\"/Unattended-Upgrade \"0\"/g" /etc/apt/apt.conf.d/20auto-upgrades

If they are already turned off the command will not do any harm, so if in doubt issue the command.
Finally, manually update your server using the procedure in THIS post.
Once automatic updates have been turned off (and Ubuntu is fully updated), you should find that the Apache service no longer randomly stops.