AFAIK cPanel have schedulers to auto renew let's encrypt by default.
On my dedicated I can also see that option and on my shared hosting domains they also get auto renewed.
So you might want to check with your hosting provider why, its not auto renewing.
NameCheap has went on record saying that they do not and will not support auto-renewal of free SSL certificates. They support the paid certificate options that can be bought as add-ons, but free certificates are only allowed through a manual upload every 90 days.Yes, cPanel have a whole Let's Encrypt module which takes care of everything from installing the certificate to updating it when the time comes.
https://gist.github.com/Shourai/bfd9f549a41c836c99c0c660c9271df6
CPanel shared hosting on NC will renew your Let's Encrypt automatically. Have you ask to support department about this?
They have an auto-update feature, which is exclusive to paid certificates sold by NameCheap. Their excuse is that free SSL is a "security risk", so it cannot be enabled on shared accounts.So they disabled the cPanel feature to auto update to force people to actually purchase certificates or some other reason, what a shame.