Time machine backup "fails unexpectedly because of lack of disc space," even though there is enough disc space for backup?

I have repeatedly tried to backup my files, but at the end, I get a message that says "backup failed unexpectedly; there is not enough disc space to complete backup," even though there is enough disc space to complete the backup of the files that need backing up. Next, I purchased Araxis Find Duplicate Files to make more space, and I am still getting this message. It says it would delete oldest files to make room for current backup (which it doesn't need to do), but it doesn't do that either. It just reschedules the next backup, and the cycle begins again. Can someone please advise me on this one? Thanks. It is an Omega 1 TB backup disc purchased at the Apple store.