time machine backup failed

From your DiskUtility run the Disk First Aid on the corrupt drive. If errors are found and repaired, run again until no errors reported.

Repair a storage device in Disk Utility on Mac - Apple Support

if you continue to see Time Machine has completed ... a new backup for you, or get a message saying "it can't create the backup." If that reappears it is likely the TM disk is in a state of failure.

You can reformat/initialize the drive, this will erase all data, format as GUID/HFS+ and see if it breaths new life into the drive. Then you can start a new Time Machine database on a clean drive.

If that message continues to reappear with increasing frequency, the solution would be to replace it.

Learn more about backup disks that you can use with Time Machine —https://support.apple.com/kb/HT202784

If you need to create a new backup from Mac—https://support.apple.com/guide/mac-help/if-you-need-to-create-a-new-backup-mh34042/10.14/mac/10.14

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3-2-1 Backup Strategy: three copies of your data, two different methods, and one offsite.

Boot clone https://discussions.apple.com/docs/DOC-10081

How to use Time Machine to back up or restore your Mac: https://support.apple.com/en-us/HT201250

Use DiskUtility Restore feature https://support.apple.com/guide/disk-utility/restore-a-disk-dskutl14062/mac

note: >System Preferences>Security & Privacy >Privacy>Full Disk Access

unlock the padlock, press the + button and add Disk Utility

If

Read Time Machine troubleshooting on Mac - Apple Support.

The backups probably became corrupted by disconnecting the drive without ejecting it first. Just erase it and start a new set. The disk itself is probably ok, but the backups probably ought not to be considered reliable anyway.

And I noticed that the backup disk is listed in the "exclude from backup" list - it is not highlighted/linked so I am not able to prevent the exclusion of my backup disk.

That's normal.

macbookquickstart wrote:

Thank you so much! Disk First Aid repaired the disk and I'm relieved I didn't need to erase and reformat. The links are helpful too. Much appreciated!

Good computing macbookquickstart !