Q: Time machine stuck in "preparing backup"

I use Time Machine on a hard drive connected to a Time Capsule (because another computer is backed up on the capsule's hard drive and it is almost full); everything was working fine until I upgraded to 10.12. Since then, Time Machine gets stuck in "preparing backup" for hours and never backs up anything. I have looked at similar reports with previous versions of Mac OS, and tried everything that was suggested (exclude the backup disk from spotlight, disable anti-virus scanning of the backup disk, turn Time Machine off and back on, restart everything) without success. I deleted the existing backup and replaced it with a new one - this worked, and after the initial backup, everything seemed fine, but only for a few days. There is 309 GB available on the HD, so this should not be the issue as the basic backup has been done. I can connect to the backup disk, and I can open Time Machine to access the existing backup without problem, so it does not seem to be related to a connection issue. I saw that one user reported a similar problem, but may or may not think it was related to the upgrade to 10.12; in my case, unless it is a very unlucky coincidence, it definitely seems related.

MacBook Pro 15" Retina mid-2015, 2.8 GHz Inte Core i7 16 GB DDR3, 1TB SSD