I had this issue and fixed it by uninstalling Kobo desktop software and ADE, and resetting my Kobo to factory defaults. I then restarted my computer, connected my Kobo, installed Kobo desktop software (and went through the e-reader setup)t, then installed ADE and it recognized my Kobo. I then authorized the computer, and authorized the device.
I have seen a few issues with ADE 2.0 and reverted to the earlier 1.7.2.
Version 1.7.2 is a little difficult to find,
I found it for PC at http://www.tucows.com/preview/853736/Adobe-Digital-Edition-For-EBooks
I don't know if ADE2.0 has issues with Kobo too, but it is worth trying 1.7.2 and seeing if it is any better for you..
This is a guess; but the last time I made the same guess the issues were different from any I had seen before (XP install), but the guess worked.
These issues with the Kobo sound similar to those I had with Sony PRS-350 ( http://forums.adobe.com/thread/1111732?tstart=0 )
sarracenia's solution is also similar to mattrweaver1's solution for the PRS-350 in that thread (though even more drastic).
I'm not sure how to help, but have you authorized your kobo to the same Adobe ID as your ADE? ADE can only transfer to devices registered under the same Adobe account.
Hope this helps
Ooooohhh... I almost forgot... Did you select 'Manage Library' on your device after connecting it?