Apple's Time Machine is its built-in full-system backup technology, that will back up to networked storage like Time Capsule devices, in addition to locally attached hard drives.
While Time Machine should maintain hourly backups, there are times when it can stall and not progress beyond its status of "Preparing backup..." You can see this status show in the Time Machine menu extra, as well as in the Time Machine system preferences.
There are several reasons why this may happen, including if you have not backed up in a while, your backup drive is full, problems with the current backup instance, and faults with the backup drive as a whole.
Lack of Backups
If you have not backed up in a while, then Time Machine will not be able to create a quick incremental backup, as it will not be able to verify the existing backups match the state of your system. Therefore, it will perform a "deep traversal" of your system, which may take a long time. You can usually see this by going to the system console, and searching for the process "backupd" (the Time Machine background process). With messages from this process listed, you can see if the most recent activity involves "deep traversal" or similar deep scans that may be the cause for the hangups.
Full-time Machine drive
If your Time Machine drive is full, then the system should regularly purge files from it to make room; however, this may also take time, especially if you have inherited the drive and its backups from another system. In these cases, Time Machine may take a while to clear out enough of the prior backups to fit any new data to be backed up from your system.
If these problems are the case, then you should allow Time Machine's hangup to resolve itself over time. Give it a number of hours (perhaps a day) to fix itself, and then see if progress resumes as usual.
Faults with the Time Machine drive
Beyond these problems, you might be experiencing several issues with Time Machine. The first is if the Time Machine disk is experiencing formatting problems. In this case, try using Disk Utility to check your Time Machine drive for errors, and fix them if any formatting issues are found.
Faults with the current backup
Lastly, the current Time Machine backup may be experiencing a fault or two that is stalling the backup. Unfortunately it is not easy to tell if this is happening; however, you can force Time Machine to re-try the latest backup, by removing it from your system:
- Go to the Time Machine menu or system preferences and stop the current backup
- Open the Time Machine disk, go to the "Backups.backupdb" folder, and remove the file that ends with ".inProgress" as its suffix
- Eject the Time Machine drive and detach it from the system
- After a few moments, re-attach the drive
- Manually initiate a backup from the Time Machine menu, if one does not begin automatically
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