I know our office is not the only place with this problem, because we found a
reference to it on a web search, but the reference had been deleted.

What we are doing is, I made a copy of a file that works and deleted
everything, getting an empty file that works.  Now we copy our data into that
file from a file that doesn't work, and get a file that does work.  Also, we
are copying the hyperlink base into the comments block
(file/properties/summary tab), so if the hyperlink base is lost, we will
still have the address, and can copy it into the hyperlink base when we need
it.  Another idea I've suggested is that we can save the hyperlink base at
the beginning of the spreadsheet, and I could write a macro that runs when
the file opens, and uses the value in the cell to set the value of the
hyperlink base.