Costs for regular software updates

For a while I build for my clients sites using WordPress platform.

Periodically WordPress update to a new version and now having in my portfolio so many sites so, when I realize I tend to update them (although with the fear that the upgrade could create problems to the functionality of the site or any plugin).
Besides this, for security reasons, it is often request also by the servers operators.
Unfortunately the sites are much now, so I was wondering if it was not appropriate to define the procedure updates by contract, to have at least a minimum of (money) to dampen my time (I do not want to spend the rest of my life upgrade the sites of others for free)
I was wondering if others have similar situations and how they behave with their customers