Check the Kobo isn't full, and that you can copy files to it using your file manager (Windows Explorer/Finder or whatever).
Check that the Kobo is registered with the same AdobeID as the computer.
Did the writing work before and now stopped, or did it never work?
There are lots of bugs in ADE2.0. Try replacing ADE2.0 with the older but more reliable v1.7.2.
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