I am having the same problem. Not only does it keep reinstalling but it keeps randomly reopening. Pretty much every time I return to my desk after walking away, the Object Desktop window is (already) open (again). It shows up in my Programs and Features control panel applet as Object Desktop, and I've uninstalled it 3 times in the last 24 hours.
Here is what the "Object Desktop" app looks like (see right):
Note the first line that shows I don't actually have Object Desktop, which presumably is a different installer than this "Object Desktop" showing it. I feel like I'm caught in some kind of recursive mirror world just trying to describe this.
This alternate "Object Desktop" -- which actually doesn't appear to be Object Desktop, which I don't have for a license for, or even have installed, based on the "fake" Object Desktop summary that keeps auto-opening -- seems to duplicate a lot of the functionality that was in Stardock Central.
So I think this may be related to Stardock Central. At some point did this alternative "Object Desktop" app/wrapper replace Stardock Central? I do have Stardock Central installed. The problems started to happen when it said there was an update.
I don't want to have to uninstall Stardock Central, I want to keep my apps up to date. However, I also don't want this dang window to keep popping up.
I thought it might be a successor to SDC but was popping up a window because I hadn't entered login info yet. So I entered it. That just eliminated the login popup but not the app appearing all the time.
I've never had any trouble with any Stardock software, and I'm one of the original customers from WAY back, but this very frustrating. These apps are supposed to make my desktop easier to use, not create problems of their own. The frustration is partly because there appear to be two different products now called Object Desktop, and they even have the same icon (as seen in the image above).
I'm thinking Stardock Central has been renamed to Object Desktop (too) and this brand change has broken the upgrade process so it's not uninstalling the old (SDC) installation? And the new one (OD wrapper thingy) has some really annoying bug that it keeps popping up this window every few hours?