I did everything I could to duplicate the problems people are having. In the end, I was able to duplicate both Airport devices being available only after restart, and only for a short time, to not being able to see Airport devices at all.
After using the windows Program and Features to uninstall both iTunes (Had the latest downloaded) and Airport Utility (5.6.1). Reinstalling netted the same issues. It wasn't until I uninstalled again, but using IOBit Uninstaller (Or similar if you trust it). I DO NOT WORK FOR APPLE OR IOBIT. I've been an Tech for almost 30 years, as well as Lw Enforcement. (IT stuff when IT isn't available and more for some extra vacation cash)
Anyway, what the IOBit Uninstaller does is use the programs individual uninstaller. Anyone who's worked with Windows knows, no standard uninstaller cleans up completely. In this case, some of the Bonjour DLL's and registry entries were left behind.
IOBit Uninstall will prompt you to create a restore point in case of issues. Do that. Use it to uninstall both iTunes and Airport by clicking the Batch Uninstall checkbox in the upper corner, then select both itunes and airport utility. It's also useful for removing trial software and other bloatware that may have come with your machine, freeing up hard drive space. Since you're going to let it create a restore point, you're at little risk for any problems.
I'm finding version differences between computers, so this may be the culprit along with rogue entries in the registry left over from the constant iTunes updates.
When it's done uninstalling each, it will ask if you want to do a power search for left over files SPECIFIC ONLY TO THE PROGRAMS UNINSTALLED. Do it. Let it scan for the files that the installer log shows remain as well as the registry entries. The registry entries are important because it could be messing with Bonjour having it stop, even though the service.msc shows it running.
This will clear everything out regarding the installation of these two programs, but WILL NOT remove your iTunes library. I do, however, suggest deactivating iTunes prior. I've not had any issues with it being activated after the reinstall, but I'd rather not use up one of your activation's if not necessary.
After this is complete, reboot the computer. This will ensure the System no longer even see's Bonjour as a service. Install Airport Utility 5.6.1 and give it a go before installing iTunes. If it works, wait a reasonable amount of time and try the airport utility again. If it still works, install the latest iTunes. Try airport utility again, and all should be good.
If you have an Apple TV or other ios device, Home sharing is pretty awesome as long as your computer is running. I bought a cheap HP core 2 Duo with a 120gb Solid state drive that uses little power. Windows 7 is installed with iTunes and I have it mount the Time Machine and Airport Extreme hard drives. They mirror each other, so the HP has home sharing on, but shares the media from the networked devices. It's a low power machine, so leaving it on and setting the power options to low power but not to sleep nets a whopping 12-25 watts under normal uses. That's less than the time machine!
Keep me posted on your progress.