In some cases cPanel will not show the databases in cPanel>>Databases>>MySQL database; though the database is present in /var/lib/mysql/ folder with the contents in it, hence it is clear that the database are not lost from the server.
The issue is due to the permission conflict to the folder /var/cpanel/databases/, the permission should be 755 for the mentioned folder.
root@server[~]# ls -ld /var/cpanel/databases/
drwxr-xr-x 2 root root 69632 Feb 16 08:15 /var/cpanel/databases/