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If you clone a volume that you backup with Time Machine, its UUID will change and Time Machine will no longer be able to make backups of it. However, it won't tell you directly what the problem is. Rather, you will find entries like the following in /var/log/system.log:
1backupd Backup failed with error: 12
2backupd Error (12): Link of previous volume failed for macosx.
If you want to continue to backup to the same volume in your Time Machine backup database, the following script allows you to change the UUID of the existing backups, leading Time Machine to backup as if the volume's UUID had never changed.