Disk Utility First Aid Fails on Time Machine Disk I've been backing up my Mac with Time Machine on an external hard drive for several years. I recently plugged the external drive into my Mac, it spent a long time running fsck_hfs and finally showed this dialog: 



Running disk utility gives a lot of Invalid extent entry messages along with the conclusion First Aid process has failed.

 

My intuition would be to copy the whole disk to a new drive. I have a vague recollection from learning about Time Machine several years ago that this would have to be block-wise in order to preserve the Time Machine backup (using dd or carbon copy cloner, right?). But presumably a block-wise copy of the drive would copy the extent errors as well?  So do I just have to give up and lose my entire Time Machine history at this point?
Time Machine makes extensive use of hard (as opposed to symbolic) links (for eg "this folder is the same as yesterday's backup").  See eg http://www.baligu.com/pondini/TM/Works.html.

I thought the issue with copying backup history was that many copy tools won't see the hard links, so you end up with multiple copies rather than links and run out of space, hence your recollections about doing a block level copy instead.

But now I look it up, apparently Finder can copy a Backups.backupdb folder correctly.  See eg http://www.baligu.com/pondini/TM/18.html (which is sadly a little out of date), and Apple's current documentation https://support.apple.com/en-gb/HT202380.

The message in your first screen shot says "You can still open or copy files on the disk, but you can't save changes to files on the disk". So perhaps you will be able to follow the instructions above to copy your Backups.backupdb folder (containing your backup history) to a different drive.