Time Machine completed a verification of your backups. To improve reliability, Time Machine must create a new backup for you since upgrading to El Capitan, every time my machine tries to make a backup to my Time Capsule, it prompts me with the aforementioned message.

after researching and finding not much, I decided to blow away my long history of backups and create a new one as suggested.  the backup succeeded but the second time it tried to do a backup it failed again.

so now I have to create a brand new backup (of the whole disk) every time I want to make a backup?

this worked fine on Yosemite!

help?
so the problem was Apple's after all.  they never admitted there was a problem but the latest firmware upgrade for the Time Capsule fixed the problem.  it hasn't failed to back up even once since the upgrade