Most often that means the packaging process has encountered one or more files which can't be copied; and that is ususally because they are open, in use, locked, read-only, etc.; essentially the same conditions that would prevent their copy at the OS level.
The other common problem that causes this is an "illegal" character in either a file name or folder name, like a \,/, or *.
Diacritics for characters used in some languages can cause this, too, I think.
As it turned out, I had one graphic that I had created that was the source of the problem. It is a 48 page magazine, so it took a lot of trial and error to find the graphic. To solve the problem, I opened the graphic in Illustrator, resaved it, then relinked it in the InDesign document, and it packaged without any difficulty. The peculiar thing to me is that InDesign showed no missing or broken links and no errors.
That's a new one. Damaged files don't show as anything special in the links panel, though, so that part is no surprise.
For the future, you could have isolated the page in a matter of minutes by using the divide and conqurer method of trouble shooting. To do that you divide the file in half and try the process again on each half. For each art that fails, you divide it in half and retest.
Once the page is identified, you can do the same to remove objects.
Thanks Peter, I did use the divide method. With a 48 page magazine and all
its photos and graphics, it is still a bit of a rabbit hunt. I never did
find any obvious problem with the errant file---opening and then re-saving
it took care of whatever was creating the issue.