The wireless controller wasn't being recognized, even after installing the latest official version of the driver.
A short search lead me to this post which explains how to tell Windows which driver to load. I deviated a bit from the steps presented here, as I found it easier than trying to find the right driver in the long list of drivers that ship with Windows.
- Unplug the xbox 360 usb wireless controller.
- Download the latest driver. Go to the Microsoft download site and download the latest Xbox 360 Wireless Controller for Windows driver for your platform.
- Run the installer (next, next, next, finish)
- Extract the driver to a temporary location using your favorite archiver (I used 7-zip)
- Open the device manager and force uninstall all "unidentified devices" so that you know exactly which driver to update when you insert the wireless controller.
- Plug in the the xbox 360 usb wireless controller
- Refresh the device manager
- Look for an unidentified device right-click it and choose "Update Driver Software" from the context menu
- Select "Browse my computer for driver software" and browse to the location where you extracted the driver software.
- Browse to the following folder: "[Extract Location]\xbox360\setup64\files\driver\win7" and select that.
- You're offered 3 different options, choose the one that says "Xbox 360 Wireless receiver for Windows"
- If a warning pops up that the driver might not be compatible with the device, ignore it and install the driver anyway.
Your wireless receiver should now work just fine, even after you unplug it and plug it back in.