I was trying to edit the Time and Date utility as launched by double-clicking on Stardock's Object Dock. I tried it after directly invoking the Time and Date utility and changed the service to time.nist.com and it updated the system clock on demand. I will know in two days whether or not that fixed the problem. For the time being, unless time.microsoft.com is unresponsive, I think we can assume that the problem lies elsewhere. For example, I have two RAID drives on USB that I use for automated backups using Acronis, and have a dedicated data-only HD as an internal drive.
Anything that comes to mind is welcome. I need to solve this problem so I can start one of my weeks-long number-crunshing sessions. This computer exists to perofrm number-crunching duty, and the requirement to boot every two days to keep the antivirus working conflicts with this.