Alpha Inconsistently Recognizing USB Keyboard

My new Alpha has been having a bit of trouble recognizing my Apple USB Keyboard (this one).  

When I plug in my Apple keyboard to the rear USB ports of my Alpha, it will sometimes work (maybe 1/3 of the time) and sometimes not respond at all (maybe 2/3 of the time).  I've never gotten it to work on the front USB ports. 

• When it works, Windows will make its "new hardware added" chirp 1x, possibly followed by a "hardware removed" chirp 1x. 
• When it doesn't work, Windows will make its "new hardware added" chirp 1x, followed by a series of "hardware removed" chirps.  Sometimes it makes just a few "hardware removed" chirps, other times it will keep making them continually until I unplug the keyboard. 
• When the keyboard doesn't work, I can usually eventually get it to work through some combination of unplugging other USB devices and re-plugging in the keyboard. Sometimes this takes 3-4 tries. 
• I'm also using a Logitech M525 mouse, using a unifying receiver.  When I'm connected to my Mac Mini, I typically have the Logitech wireless receiver plugged into the USB port of my keyboard, but I've never gotten the keyboard to work with the Logitech mouse plugged in to the keyboard's USB port.  For this reason my suspicion is that the issue is something to do with the keyboard being both a keyboard, and a USB port.  
• I've tried installing Apple's bootcamp keyboard drivers, but that didn't help at all.  So after re-installing Windows when I upgraded to a SSD, I found that I had more success without the drivers.  

Any ideas what's going on, and what I might be able to do to fix it?  I'd eventually like to use a KVM to make the switch easier, but I'd like to figure out how to get things working consistently when plugged directly into the Alpha before I go that route.