Have you put DRM (digital rights management) books on your eReader before?
If not, you probably need to register the device.
With the device plugged in and ADE running
menu/Help/Authorize Device to ADE2.0) (menu/Library/Authorize Device to the more reliable v1.7.2).
If the device is a Sony, there are bugs in ADE2.0 that prevent it working properly with library books
(how Adobe manges to create such obscures bug I do no know).
There are other odd issues with ADE2.0, so if the authorization above does not work try ...
There are lots of bugs in ADE2.0 (and 2.0.1). Try replacing ADE2.0 with the older but more reliable v1.7.2.
(You can have them both installed at once if you like.)
Version 1.7.2, it is a little difficult to find, available on Adobe site for Windows and for Mac.
The forum software is sometimes corrupting the link above. There shouldn't be a blank in 'editio ns.html'. The following redirects to the same page: http://tinyurl.com/diged172