As has been noted in a few posts, when you plug Alpha Track into a different usb port than the one you used to install it originally, Adobe Audition sees it as 2-Alpha Track, then 3-Alpha Track...and so on.  Which leaves Audition unable to really see it at all. 

The simple solution is, of course, to plug it into the original hole you used when you installed it, but if you have a bunch of usb ports, and a buttload of usb devices, that can be tricky.

Re-installing the driver doesn't clear the registry entry and therefore will not solve the problem, and in my case Windows 7 wouldn't let me delete the registry entries that were created each time I plugged it into the wrong usb port.

But alas, after much searching I found the solution! (And it doesn't involve re-installing your OS!)

Each time you plug in a usb device for the first time in a particular usb port, Windows registers it and remembers it.  This is the problem.  What you need to do is make Windows forget it ever met that device, and here's how you do it.

First, you need to be able to see the devices Windows is remembering.  The Device Manager doesn't, by default, let you see devices that aren't currently plugged in.  Here's how you change that in Windows 7, but if you do a little homework, there's probably a way to do the same thing in your Windows version of choice.

Right Click on My Computer, or Computer, Select Properties, Advanced or Advanced System settings, and Click on Environment Variables, Hit the New button at the bottom under system variables and enter devmgr_show_nonpresent_devices as the variable and the value as 1.

Now, go to your Device Manager and under the "View" heading, choose to show hidden devices.  Now, you'll see everything that was ever connected to your computer!  Just unplug your Alpha Track, and delete every mention of it in Device Manager then plug it back into whatever usb port you wish!

At least it worked for me.  Your mileage may vary drastically.