I don't have access to my desktop computer at the moment, but I'm fairly sure it had the same version of Mids', and updated just fine with the in-game updater; the issue only exists on my laptop. Both are running Vista, and are logged in as administrator, so there should be no need to run in administrator mode.
The version on my laptop says:
Program Version: 1.91
Game Issue: 19
Database Version: 19.001 (06/Dec/2010)
Reinstalling from the build posted at cohplanner.com (which had the same filename as the most recent version I had downloaded) resulted in a popup saying "Update applied!" (I did not get that before) and Mids' opening with the new version applied.
I edit my Mids' databases; I remove the suppressable defense values from stealth powers. This is the only thing that I can think of that may have prevented the update from applying. However, I've made the same change on my desktop, and it had no issue updating.
Either way, the issue is resolved for me.