ADE sometimes gets into a semi-authorized state.
Remove all authorization using ctrl-shift-D while in ADE (cmd-shift-D on Mac), and confirm the prompt that comes up.
Restart ADE.
Try again to authorize ADE.
You will then need to authorize the Sonys as well, using menu/Library/Authorize Device to ADE with the Sony plugged in.
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If these are library books, you may need to install ADE1.7.2.
There are bugs in ADE2.0 that mean it will not operate correctly for Overdrive library books when used with several Sony readers (including PRS-350 and at least some others).
Version 1.7.2, it is a little difficult to find, available on Adobe site for Windows and for Mac.
http://helpx.adobe.com/digital-editions/kb/cant-install-digital-editio ns.html
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