First - When you installed the reader, did you download the installation program for Vista? Are you using this link?http://get.adobe.com/reader/otherversions/
If you didn't use this link and select Vista, then do that as the first attempt at a solution to this problem.
If you've downloaded the correct installation program for Vista, and it's the Vista version that is causing the file association problem, you will find someone with this same problem where the solution offered is to uninstall Adobe and then run the .exe file association fix. However your file association problem seems to go away when you uninstall Adobe, so I wonder if you could use the file association fix after the installation at that point when the problem occurs. http://forums.techarena.in/vista-help/936013.htm
Did either of the above work?