I got this error message when i clicked "Coudflare" icon in cPanel:

"Child failed to make LIVEAPI connection to cPanel."

i was adviced to upgrade to the latest version of the cloudflare plugin by executing this command on the host server (WHM):

bash <(curl -s https://raw.githubusercontent.com/cloudflare/CloudFlare-CPanel/master/cloudflare.install.sh) -k YOUR_HOST_API_KEY_HERE -n 'YOUR_COMPANY_NAME_HERE'

The API key and company name can be found in API section of the client area at partners.cloudflare.com

And indeed that helped to get rid of that error.