Thanks for the clarifying the difference between EXIF tags and XMP keywords. That put me at ease because my primary concern was that somehow the tag data was being corrupted. That's clearly not the case since the data sets are separate.
To figure out what was going on, I tested a few approaches. Some key findings:
1 - Turns out that if I use Windows Explorer to delete all previous tags associated with an old image, save the changes, and then add the tags back, then those new tags show up as expected in the Keywords section of the IPTC Info window in Photo Mechanic.
2 - I also noticed that new images that I "keyworded" for the first time using Photo Mechanic and then viewed from within Windows Explorer had those Keywords show up as expected in the Tags section of Windows Explorer. The opposite also worked in which I tagged a new image for the first time using Windows Explorer, and the tag showed up as expected in the Keywords section of Photo Mechanic.
3 - The apparent root cause though, is that I determined that all of the images which exhibited this problem were tagged years ago using an older version of Windows.
I'm guessing that one of the Windows OS upgrades modified where these Tags were stored. Deleting tags created under the old OS, and recreating them in the new version of Windows Explorer puts them where contemporary tools expect to find them - IPTC/XMP. So, I'm just going to batch delete the tags from these old images using Windows Explorer (very easy to do), and then Keyword them using Photo Mechanic. This way, all of my images have tags in a common container (XMP) that can be viewed consistently.
Problem solved