Have you tried to delete any backups in your computer? Both via iTunes' Edit > Preferences > Devices > "Delete backup" and by going to iTunes folder to verify any all backups are gone? Obviously, something has happened to corrupt your backups. Maybe if you delete the backups, then re-install iTunes (after a computer reboot)? Honestly, these are just guesses here, because I've not experienced a continual, multi-iDevice, backup problem.
Also, AFAIK, a backup is not necessary to upgrade. You can always restore your device from new. Yeah, you'll lose all the data off your iDevice, but if you save it in other places, you can put it all back on or reset everthing. Note that I didn't say easily, but it can be done. Then, I should think that a newly restored device would have no trouble, going forward, in creating new backups.
You can also choose to use that older, good, backup (providing you don't delete it in following the process in my first paragraph).
I know, not much reassurance, but it may be that starting all over right from new is your best bet. Sorry I'm not of better use and good luck.
Marilyn