So, I set up a test VM and was able to reliably replicate the problem. If I kept the VM out of the Veeam backup jobs, then the Windows update history would be fine. If I included it in a backup job, then the history would be lost. But, it wouldn't happen right away. It could be a few hours after the backup. I had been hoping for something more dramatic to show support.
Based on what I've been seeing, I think it is related to the "Enable Hyper-V guest quiescence" option (and possibly having AAP off at the same time). I tend to keep AAP off so that I don't have to give Veeam admin access to all of the systems. I had both options off on the backup job that processed my DCs due to the Server 2016 compatibility issue with down-level DCs and their Windows Update history was never lost.
However, it seems that installing KB4074837 on the VMs has fixed the issue. Since installing it, all of the VMs that got it have retained the Windows Update history going forward. That's good news except KB4074837 is not available for the R1 releases of Windows Server 2008 and Windows Server 2012, and I've still got some of those in my environment.