I manage about 50 servers mostly by remote access using ssh on a custom port (root login disabled and users need a public/private key to log in, password login are disabled).
each servers have a unique root password (long string of letters(upper/lower case), number and special characters that doesn't look like a dictionary word).
every server is kept under close monitoring for failures but also unexpected processes, behavior and hacking attempts.
there are only 3 people how knows the root password, and I know they wont write it down somewhere (for that matter, they are as paranoid as me), so I see no reason why this password should be compromised.
Knowing all this, is there a reason why I should change my root password at regular interval ? and if so, what would be a correct interval ?