Overnight Apple released an upgrade for macOS Sierra, but it doesn’t seem to have addressed the Time Machine backup issue. If you have not yet upgraded to macOS Sierra I would hold off a little longer.
I rang Apple support last week to let them know that since the macOS Sierra upgrade I could not use Time Machine. They said that there were no known issues with Sierra and Time Machine. Their suggestion was that it was probably my USB drive. We ran Disk Utility first-aid, and it threw up some errors. Their suggestion was to erase my Time Machine backup and start over again.
I have two years worth of files on my Time Machine backup so I was hesitant to do this. I also thought that it seemed too much of a coincidence that the very morning I upgraded to macOS Sierra was the morning that my USB drive started having errors.
After I got off the phone I connected my Time Machine backup to my MacBook air which is still running El Capitan and ran Disk Utility – no errors! I plugged it back into my Sierra Machine – it still doesn’t work. So Sierra is definitely having problems.
We will have to wait for Apple to acknowledge and address the problem. In the meantime, the best fix that I can see is to put your old Time Machine backup aside to keep it safe, and start a new backup on a new external hard drive. When you do that you will be prompted as to whether you want to keep backing up to your existing hard drive. Select yes, so that you now have two Time Machine backups, so that when Apple release a fix you will be able to plug in your old Time Machine backup and keep using it.
It appears that Apple have made some changes to Time Machine backup with macOS Sierra.
Here are some other place on the Internet where you can read about the problem with macOS Sierra and Time Machine: