So I feel as though I've become a bit of a guru at this issue since my magic keyboard seems to get kicked off just about every round of updates for a few months now. However, it seems everyone has their own system for getting it to work, so I wont say this is a fool-proof solution:
Disclaimer: This has only worked for me after having successfully installed the keyboard on the OS previously; my bet is that most of these posts are in the same boat, and that this issue is the result of the Bluetooth driver picking up a present signal when Windows 8.1 doesn't (since my keyboard driver shows up in device manager even after I've "forgotten this device" in PC settings.
1. Turn off your Bluetooth keyboard by holding the power button until the light turns off. In the name of good tech-support I'll also say that if the keyboard was already off, then you will see the light come on and then start to blink. This is pairing mode for those who did no already know.
2. As many have said, uninstall the Bluetooth driver in Device Manager (either under Control Panel > Hardware and Sound > Devices and printers > Device Manager; or Ctrl + X > Device Manager) by opening the drop-down menu under "Bluetooth" and right-clicking the Apple Broadcom Built-in Bluetooth. Also uninstall the keyboard's Bluetooth driver if it happens to show up in the list.
***This may automatically re-install, but it did not disrupt the process for me***
3. Restart the computer, leaving the Bluetooth keyboard turned off.
4. Go to Bluetooth in PC settings (either by right clicking the Bluetooth icon in your toolbar and selecting "Show Bluetooth Devices" or under Ctrl + C > Settings > Change PC Settings > Bluetooth).
5. Hold the power button on your Bluetooth keyboard until the light begins to blink for pairing mode.
***It was at this point during my attempt that my keyboard automatically showed up as paired and began to work properly***
6. If your device had been successfully uninstalled from Windows previously, you may have to re-pair by clicking on the keyboard and then "Pair" while your keyboard's light is blinking. You should be prompted to enter a serial or to press a series of numbers followed by the enter/return button.
If this works for just one more person I'll be satisfied for having posted this. It's been driving me crazy and I always forget how I got it to work the time before.