I'm not familiar with the Accordance program so this is just a guess, but
since it's probably not intended for its users to re-write the Bible it may
be that the content is not editable even if it's selectable. As a result you
may get the impression that you're copying but nothing goes to the
clipboard. Other possibilities exist as well, but more detail about OS
version & the Accordance app (locally stored or on a web site, type of file
viewed in the app, etc.) would be helpful to know.
In the meanwhile, have you tried pasting into other types of files - such as
TextEdit? What happens if you do?