[FOLLOWUP TO PREVIOUS MESSAGE]
It seems my failed backups were somehow related to saving web pages in my email. I now realize I began having backup problems about the same time I began using the SAVE feature for webpages. After the successful backup, all my saved pages were deleted - obviously that's what you're deleting when you clear Browser Messages.
I tried saving a page and seeing if that caused the backup to error out, but it worked OK - so it's more complicated than just having a webpage saved.
But next time I can't back up, I'm going to manually delete saved webpages to see if I can discern a pattern.