Even though Time Machine is very good at backing your Mac up, it sometimes has problems in completing backups. One of the simplest errors to fix is “the backup could not be completed because the disk could not be found”. This error can persist until you make some drastic move, like completely erasing all old backups. But a simple solution can save you a lot of trouble.
Our TM images are on the Synology Disk Station, which generally does a great job of impersonating a Time Capsule. The TM backups are on separate volumes that have their own users and logins on the Disk Station. Go to Keychain Access and remove the TM network login from the login keychain (just delete it). Now login to the backup volume and again, and re-store the password.
Some Time Machine problems are more difficult to fix, but there is an encyclopedic resource for that. Wow.