I had a similar problem with my iPhone 6 (iOS 9.2.1) and iTunes (12.3.2)
I tried deleting the previous back-ups, but the problem kept coming back. It got to a point where i could not even backup even after I had deleted the back-ups via iTunes/Preferences/Devices. I had to go into ~/Library/Application Support/MobileSync/Backup to figure out which was the backup for my iPhone and delete that particular folder. Even then, the problem came back after I had backed up the phone once.
I came across another thread and it got me thinking that it could be a corrupted app that is causing the problem. I went through all the apps on my phone to try to figure out which was the one i had installed recently that may have caused the problem. And then i found it. It was an app that i had installed outside of the AppStore. I figure since Apple curates the apps stringently, it is unlikely (but not impossible) that they would allow one in that might corrupt the ecosystem. So i deleted the offending app, and tried again, and lo and behold, everything worked as it should be!