Hi All,
I haven't had chance to read what everyone has written but I've glanced over and seem to think I can add some further information, however, not a solution I'm afraid!
I have a MacBook Air (2013) and an iMac (2016) - the issues started last year for me on my iMac (at this stage I wasn't syncing my MacBook Air). I phoned Apple and as I was still in warrantee they sent me a refurbished time capsule replacement saying that there was clearly a problem with the time capsule itself. Thought this had fixed it, but still the same error presented itself a couple of weeks later. I tried calling the person who said I needed a new time capsule and he didn't bother replying to any of my e-mails or returning my answerphone messages. After much complaining I got through to someone who said this was a new issue and that it should be sorted by the next update... a few weeks later, said update came, but the same error arose a few weeks after that. After numerous calls, I was asked to set up a new profile on my iMac to see if the error presented itself again (at the same time I set up my MacBook Air on the same time capsule) - after about 3 weeks, both were still updating okay and I was told that setting up the new profile had fixed the issue on my original profile, as such, I retuned to my old profile and deleted the temporary one. In fairness, I've gone about 5 weeks this time, however, the same error has presented itself a few days ago, but on the iMac only.
The interesting thing is that both of my systems are running the latest Sierra. Also, for some reason, Disc Utility will not accept my time capsule, so I cannot attempt a repair. In addition, on Disk Utility there is a padlock on the image of my iMac but not on the image of my MacBook Air?
The person I was dealing with in Apple believed that there was an issue in the software that only affected some people - she thought that it has corrupted the user profile - I'm currently waiting on a call back from her, but I think I may have to just set up a new profile and move all of my stuff over and hope it doesn't move the error.
Sorry for the overlong post, but hopefully this provides some new information?
Stephen