Sebastian, thank you for your help. I finally figured out what was going on. I'll fill you in just to document what I found.
I created a new site to go with the DNN version upgrade. There were significant design changes as well. So, I created a second portal for the new site.
In order to keep the User ID's and passwords from the old site, I created a Portal Group and connected the two sites. I had the old site as the "Parent" and the new site as the "Child."
The password reset link sent the User to the new "child" site and it was not working. When I used the same syntax but pointed to the "parent" site instead, the link worked. I'm not exactly sure why.
I really don't want them to go to the old site once this change is in place, so I changed the parent-child relationship in the portal group. I need to make some other changes to the user profiles, etc. But, the password reset link works just as expected!
Thanks again for your help in troubleshooting this. Your questions got me going down the right path.