I have the same problem
If these are library books you are lucky. Wait for the loan to expire (you wn't be able to return it early while you have this problem) and borrow it again.
More stuck with bought books.
This is a vicious trap that Adobe lays for unsuspecting customers.
They do give very mild warnings, but not nearly strong enough.
When you register 'without ID', ADE creates an anonymous/implicit ID with limited powers (eg can't be used to share with other devices).
Whenever you first load a DRM book, that copy of the book is associated with whatever ID the computer is registered to at the time.
Any book you load while this anonymous ID is active gets associated with that ID, and can't be read on any other device.
When you properly register your computer with a real ID, that old anonymous ID is lost.
Now you don't have any devices that can read the book.
Not appropriate for you, but for completeness .....
The only way I know round this is to use a DRM stripper such as epubee BEFORE you deauthorize the device.
I do NOT advocate using such code to get around the valid limitations placed on a DRM book.
However, where the problem arises only because of the ineptness of Adobe's ADEPT DRM infrastructure and its implementation,
such a measure is totally justifiable.
This whole ADE thing is such a frustrating disaster!!! I spent almost an hour trying to download an library ebook to my NOOK. I've installed software. Create stupid Adobe account. Waited 15 minutes for the confirmation email. Now I've learned I am screwed because I have make an irreversible mistake of registering 'without ID'! Good to know I can wait 21 days for the library loan to expire. The non-Kindle ecosystem is so f**k'd with this unusable UI. Death to DRM
Try this (it worked for me):
1) In ADEditions, go to Help --> Erase Authorization
2) In ADEditions, go to Help --> Authorize [using Adobe ID]
3) Select Book(s) --> right click --> Remove from Library
4) Re-add book(s) (in case that you have an .acsm file with a link, open this file with ADEditions)