You may recall the problems I had with my Microsoft Fingerprint Reader when it was plugged into my Belkin F5U237 Hi-Speed USB 2.0 7-Port Hub; after a few successful reads, the device would simply stop working. However, if I plugged it directly into the USB 2.0 port on my motherboard, everything worked just fine. Although I didn't mention it, I later found that anything plugged into the hub would eventually fail. In my post, I said that I would try another hub, so I purchased a second Belkin F5U237, and the devices exhibited the same problems. Frustrating, but enlightening.
After doing a little internet research, it appears that the VIA USB 2.0 products (VT6202, VT6212) have some known issues. I tried many of the suggestions (including VIA's own Filter Driver) to no avail, so I purchased an Adaptec USB2connect 5100 6-port USB 2.0 card and installed it in my new computer. I'm happy to say that everything now works perfectly through the Belkin hub, and I have a lot of available USB 2.0 ports. :)
I hope this post can save someone else a few hours if they run into the same problem.