The Solution to "Time Machine Couldn't Complete the Backup"

When using Time Machine to backup data to "Backup_Machine" disk, it shows the error message "Time Machine couldn't complete the backup to xxx" above and discontinues the backup operation.  It indicates that it might be the disk problems or file corruptions.  The message also suggests to run Disk Utility to solve the problem.

Disk Utility

So, The first thing is to run Disk Utility to check and repair all files and disk volumes if they have problems.  There are two steps to do so:

1. Run the Disk Utility within the system.
2. Run the Disk Utility in Recovery mode (press Command（⌘）and R when booting) .

After running Disk Utility and getting positive result, Time Machine backup operation should continue without any error.   If the problem remains, it shows that there is at least one corrupted file which can not be fixed by Disk Utility.  

The Time Machine Mechanic (T2M2)

The solution is to find out the corrupted file and exclude it from backup operation.  However, the error message from Time Machine does not indicate what exactly the corrupted file is. Fortunately, there is a sweet utility called "The Time Machine Mechanic (T2M2)" written by a friendly person who save our lives.  It shows the system log related to the backup errors, the file name and location.  Therefore we can exclude it from the Time Machine backup operation (see more details). 

If the problem shows again, just run T2M2 and add the file to the excluding list of Time Machine.  Rerun Time Machine again until it completes the job.

Note: The error of Time Machine is "BACKUP_FAILED_COPY_STAGE".