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.