Downtime is inevitable: servers need to be updated, patches applied, hardware upgraded or fixed, and so on. But how do you choose when to take the server down (if you have a choice)?
First of all is to ask the affected users of the system. This can range from getting the supervisor or person in charge to give an OK to having meetings with all affected. In some fashion, the users who are affected need to know and need to have input into the best time to take the server down. When the server is down, they may not be able to do much of their work; minimizing impact on them is important.
To also minimize impact, the downtime can often be arranged during off-hours. In the U.S., this is typically outside of the normal workday of 8 a.m. to 5 p.m. (800-1700). However – if the server is in use in other time zones, this window gets bigger – and if the server is used world-wide, the window gets bigger still.
The other thing to think about is which day to take down the server. One can do it during the work week (Mon. through Fri.); however, all of those nights (except Friday) are constrained by the fact that the availability deadline would be something like the next day at 7:00 a.m. When downtime is scheduled for Friday night, there are two entire days more to get things right. If a downtime is necessary for a major upgrade or extensive changes, then scheduling for Friday night gives that much more time to get everything working before Monday morning.