If too many registrations is the reason, it may be best to use the customer's registration.
I guess most customers would trust you with their Adobe Id.
If you choose ctrl-shift-D to your library copy of ADE, that will deregister your Adobe ID.
Restart, and it will ask you to register an AdobeID.
Enter the customer's details; or if they haven't got an Adobe ID yet will give them a chance to get one (with your help).
If they've got their eReader with them you can even authorize that for them form ADE with their id at the same time.
When the customer is gone; go through the ADE deauthorization again, and reregister it with your id.
(ADE DRM isn't very clever, but I think it is clever enough to recognize the same device reregistering.)
I'm not sure how much time you have to spend with each customer, so what I say may not be practicable.
The whole Adobe DRM mechanism can be pretty daunting even to computer literates,
I guess you must have quite a job helping some library customers with little computer experience.
You may be able to get additional registrations as a librarian; see useful post at http://www.lincolnlibraries.org/databases/How_to_Request_Additional_Authorizations_From_Ad obe.htm
If that fails, at least their support should reset your existing ones.
What you suggested was spot on. Its now working again
Thank you so much