Prevent Server Restart after Windows Updates

In group policy for the server, navigate to:

Computer Configuration->Administrative Templates->Windows Components->Windows Update->No auto-restart for scheduled Automatic Update installation

You can get to this by running gpedit.msc.

Reboot to apply changes.

Don't forget that your server won't be updated until you reboot and will be vulnerable to the threats!

You can accomplish this, and leaving updates installed waiting for a reboot does not leave the server in an inconsistent state. Updates that require a reboot are not applied until the reboot occurs. The settings to manage automatic updates are too numerous to list here, but you can manage them in a domain via Group Policy, or on stand-alone machines using Local Policy. Go to Computer Configuration>Administrative Templates>Windows Components>Windows Update.

The best solution that I am aware of is to turn off automatic updates. Then you schedule maintenance windows with your customers and apply the updates manually and do the reboot then make sure everything that you need is running after the reboot.

Just stopping the reboots is a bad idea because that gives the impression that you are fully updated when you really aren't since updates that need reboots to complete...well...you know...need reboots to complete.