say the patch unexpectedly breaks another critical function of the server.
When this happens, it usually takes a lot longer to fix than it takes to drive in to work, because the way it breaks is unexpected. The proper method is to have an identical server get upgraded with this automatic maintenance window method the day before while you're at work or at least hours before the primary system so that you can halt the automatic method remotely before it screws up the primary system. If the service isn't important enough, let your monitoring software wake you up if there's a failure or ignore it until you get in at your normal time. Most of the time, having a regularly well-rested sysadmin is more important to a company than having "light-switch monitoring server three" running between 4AM and 8AM.