I have figured out why this is happening.
With the WiX installer being compiled on a x86 platform, Windows 7 picked it up as the 32-bit installer with 32-bit registry keys. Windows 7 64-bit handles 32-bit registry entries by doing just what I saw happening.
The program was still registered; it was just not in the 64-bit portion of the registry. Compile it under a x64 platform while making the necessary changes to make it for a 64-bit system (ProgramFileFolder become ProgramFiles64Folder, etc.), and it will put things in the right place.