cPanel has an option called "Cookie IP Validation". This setting checks that the IP address that the visitor originally came from matches their IP address on subsequent requests. With Cloudflare, the IP address for requests to your server can variably come from any IP address in the list at https://www.cloudflare.com/ips
The solution is to access the cPanel server on a URL that doesn't proxy through Cloudflare. Please use the URL http://cpanel.YourDomain.com
Make sure this subdomain is not proxied through Cloudflare (not orange clouded).