Time Machine won't back-up due to "The backup disk image “Valerie’s MacBook Pro.sparsebundle” could not be accessed (error 19)."

We need more information to be able to help. That means some questions, which will likely be followed by more questions depending on the answers to first set of questions.

What device are you backing up your Mac to? Is this an Apple AirPort Time Capsule, or another brand of hard drive?

We assume that you have already performed basic troubleshooting steps like powering off the backup drive, restarting your Mac, and powering up the backup drive again, correct? If not, that would be the first thing that you would want to try.

Thanks for the info.

If no luck powering off the Time Capsule, Mac and restarting, etc......

Hold down the option key while you click on the Time Machine "clock" icon at the top of the Mac's screen

Select Verify Backups and run the diagnostic check

The process might take anywhere from 10-60 minutes or more to complete, depending on how much data is stored on the Time Capsule hard drive. Let the process run until it completes successfully.....or....until you see an error message appear.

If an error message appears, please post back with the exact text of the message.

You can watch the progress of the Verify Backups check if you want by clicking on the Time Machine "clock" icon at the top of the Mac's screen and then clicking on Open Time Machine Preferences.

Unfortunately, your backup file has become corrupted and is no longer useable, so you'll need to erase the Time Capsule disk and start over again with a new backup and move forward.

Click "Erase Backup History" to start the process when you are ready.

With luck, things will work OK for the next year or two.

Good luck. The Time Capsule hard drive starts to become "suspect" at about 7-8 years, so hopefully things will work well for another 2-3 years.