Xcode Update 5.1.1 issue

Upgraded to OSX 10.9.2 on Macbook Pro 17" Early 2011. Since then, there were a number of apps that presented in the App Store for updating. I clicked "Update All" every time, and haven't had any issues. Just 6 days ago, 4 apps required updating, including Xcode 5.1.1 -- but it's the only one that won't really do anything. I turned off asynchronous updating, went back, and no change in behavior: clicking the "Update" button directly just shows the busy-wheel for about 2 seconds, then re-enables the Update button.

Going onto the Apple site and looking up the Xcode app for downloading, it seems to know that Xcode is installed, and the "Install" button changes its caption to "Update". Clicking that produces the same behavior.

I've rebooted, with no behavior change.

I ran Xcode, and it said that some dependent components needed to be installed, and I let it do so; the About shows I've got version 5.1 installed. In the Launchpad, It still shows that there's 1 update required in App Store, and it remains Xcode 5.1.1; nothing seems to change this.

I don't want to uninstall Xcode 5.1 -- I just want it updated.