In the contrary: Copyright can be strengthened by not publishing
Unpublished works are protected the same as published works and usually, that is the author's death+70 years. In some cases - unpublished and author unknown - it is creation+120 years and corporate published works are 90 years.
While copyright lasts, the law dictates that it is the absolute exclusive right of the copyright holder to make prints outside of some exceptions. Whether they are printing the work or not does not matter: as long as the right lasts, it's exclusive. The act of refusing to sell a published item does nothing for the strength of their claim in itself.
On the other hand, refusing to publish an unpublished work does strengthen their claim for damages, as an unpublished work that Alan illegally brought to market does not need to be registered - it is still unpublished for the courts!
In the context of the question, the work has been published, but not offering it does not lessen Brenda Books' claim that it was an infringement.
To overcome the infringement claim as the defendant, there might be a fair use argument by satisfying the balancing test, but the copyright owners' rights in the text are not diminished by there possibly being some ways that allow republishing part or the whole of the work within the confines of fair use/fair dealing.
The problem for Alan is, that unwillingness to grant a license and then not being able to prove fair use/dealing means he should be well aware that he is infringing, possibly even stepping his problem up to wilful infringement in case fair use/dealing is not found. in the US can be penalized with 150 000 USD plus attorneys fees.
A rough estimation of the fair use factors:
- Making copies for sale would weigh extremely against Alan, for archival purposes it would weigh for Alan. (see Authors Guild v. Google, Inc., (2d Cir. 2015))
- The amount taken, impact on the market, and nature of the work count against Alan - making a finding of fair use very tricky.
But.... how did Google get away with copying the whole books? It hinges on the whole copy being searchable, very much transformed, and that the users can't get access to the full text as long as the work is under copyright. From the court of appeals' judgement on the Google case:
(1) Google’s unauthorized digitizing of copyright-protected works, creation of a search functionality, and display of snippets from those works are non-infringing fair uses. The purpose of the copying is highly transformative, the public display of text is limited, and the revelations do not provide a significant market substitute for the protected aspects of the originals.
A rough look at the fair dealing factors:
- The purpose of the copy might cut against Alan most of the time, the mere usage type cuts against, use is ongoing, the whole book is copied, the means are not exactly required, the nature of the book cuts against and it is market usurpation...
In short: I don't see how Alan might manage fair dealing unless it would be very much the Google Books example. Making copies even for a 0 profit would not fly.