Sometimes mail server IP gets blacklisted in the RBL's which causes inconvenience to send / receive emails. To overcome the problem, the mail server IP can be changed so that emails will work fine.
To change mail server IP in WHM cPanel:
1) Login to WHM and got to WHM >> Main >> Service Configuration >> Exim Configuration Editor >> Domains and IPs , enable option "Send outgoing mail from the ip that matches the domain name in /etc/mailips"
2) Login in the server as a root user using shell and open file /etc/mailips for editing which will display something like this
Replace 220.127.116.11 with the new mail server IP and save the file.
3) Restart exim service
If any feedback, queries are always welcome!