Try doing this via:
Control Panel > Default Programs > Set Associations
I had this same problem after uninstalling 5.5 on my machine(s). I fixed it by re-installing CS6. If you google, you will find a registry hack you can do, but it didn't really work for me very well, re-installing worked like a charm.
Admiral Cook, I tried to follow your method but Premiere Pro was not available in the list of Default Programs.
If I reinstall CS6, that will take me back to 6.0.0 (original install files before the update). Looks like going backwards might be the only way to get this fixed. Sigh.
Yeah, to get it back on the list of default programs you have to edit the registry, or re-install. After you re-install, you SHOULD be able to do the updates and retain your file associations - worked fine for me.