You wouldn't schedule downtime for the middle of the day. You schedule downtime during your period of least usage.

You design the complete system so it does not have dependencies on a single component, that way each subsystem can have proper maintenance schedules. It takes a lot more up-front work, along with defining what levels of service degradation are acceptable during a window, but that's the difference between a professionally run service and one run by amateurs. Look up Google's SRE methodology and their concept of error budget.