Visiting a website reports a failure to connect such as:
The requested URL could not be retrieved
Connection to $IP_ADDRESS failed.
The system returned: (111) Connection refused
If you are able to perform a Nmap test to the affected domain, you can determine that the problem is that the HTTP ports are responding as "Closed".
nmap -Pn -sT $DOMAIN -p 80,443 --reason
Since the HTTP ports are "Closed" they are indicating that nothing is listening on the server end and thus
Make sure that the IP address that the website is using is not an IP that is listed as reserved.
WHM >> IP Functions >> Show/Edit Reserved IPs
Or in the following interface:
WHM >> Apache Configuration >> Reserved IP Address Editor
Please note that any IP address that is added as "Reserved" will not be listening on Apache, thus the website will not work.