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It is repairable, though. From macosxhints.com:
A little-known fact about Time Machine is that it depends on the MAC address of a computer to tell one system from another. This means that if you have your Mac repaired with a new logic board, or replace your system with a new one, you can't resume backups where you left off. If you know of the problem, though, it's not very hard to fix. You need to re-pair the backup to the new logic board's MAC address. Further complicating matters is the ACL which prevents you from changing the system ID information.
Here is the article.
Sometimes Time Machine will fail to back up your Mac, giving you a vague message about how it could not back up your computer.
When this happens, run Disk Utility (Applications/Utilities) and repair the volume. On my 500GB removable drive, this took three hours.