Time Machine Back Up Error

Just a quick warning: backing up items from your documents folder with a USB stick is better than nothing but so much of our data isn’t in the documents folder. Photos, music & video, and preferences data are elsewhere and depending on your collection may not fit on a single USB stick. The situation you find yourself in is one of the reasons I use a multi drive drive backup system. With two drives used for backups if one of them dies or the backup becomes damaged I still have a backup. Actually I still have 2 because I use 3 drives and one is always out of the house in case of fire or other disaster.

The exact wording of that message is important. If the source is named "Macintosh HD" and the message states Time Machine could not back up the disk named "Macintosh HD..." it is referring to the source volume. Read this Discussion for an illustrated example: Time Machine unable to complete backup - Apple Community

"An error occurred while preparing the backup".

That on the other hand can refer to a number of different causes. If there is no other obvious cause or likely explanation I'd erase the backup drive and start a new set. Obviously you wouldn't want to do that unless you created at least one additional backup on separate drive first.

That's ok. Apple designed TM to tolerate backup drives that are only connected once in a while. TM continues to create "local snapshots" that are flushed to the backup drive whenever it is connected.

I wouldn't do anything without creating an additional backup first. You never want to be without any backups at all. Having another one conveys some options.

If TimeMachine tells you the hard drive is full it is referring to the backup drive. When it can, TM will delete old backups to make space for a new backup but TM will never delete files that are part of a complete backup so sometimes TM cannot clean up enough space for a new backup set. This is why most of us recommend a TM backup drive be at least twice the size of your computer’s hard drive. This gives you plenty of room to spare. In cases where a backup cannot be made because TM is unable to clean up space you have two choices: erase the drive and start over or purchase a new backup drive. Personally, I’d never erase my only backup so I’d buy a new drive.

It should certainly not be necessary to reboot for TM to resume its activity. Perhaps the drive is becoming unmounted for some reason. Try ejecting the drive, then disconnect it from the Mac and reconnect it again. If you are prompted for a password, provide it and select "remember this password in Keychain" or words to that effect.

This is just a guess.

Try and eject your Time Machine disk, remove it from your computer and connect it again to see if the issue persists

For me, this solved The issue