( This article is of little interest to normal readers of my blog; I put it here for the benefit of folks searching for a solution. )
Time Machine backups fail if you replace a symbolic link to a directory with an actual directory. (In my case, the symbolic link was to a directory on another disk.)
The solution is to perform a Time Machine backup after deleting the symlink, then create the actual directory. Time Machine backups will then work.
Prior to finding this solution, I had tried visiting the mounted Time Machine backups in Terminal to delete the old symlinks, but the deletions always silently failed. Trying to remove the ACLs (“chmod -N”) also silently failed. It was very frustrating.