I have the same experience, win7 64bit - itunes 12.3.2.35 - iphone 6 iOs 9.2.1.
FIRST problem I encounter was after the release of iOs 9. Some of my apps I bought from Appstore now not linked to my ID. so they can't be found in my phone's appstore/purchased/ - but they are currently in my iphone (installed, been backup [save on my iTunes]).
SECOND, after iOs 9 - Any apps I downloaded directly to my iPhone won't be sync to my iTunes. So if I want to update my iTunes library, I will need to download it there. But backing up my iphone still works without any error notification EXCEPT any apps updated in my phone won't be sync to my PC
According to my iTunes my last successful backup to my win PC was 27th of Feb.
THIRD, I noticed that once I connect my iPhone to PC (where my iPhone runs the current iOs 9.2.1) - It appears to my iTunes that there is an available Os update for my iPhone named 9.2.1. Okay I egnored - I didnt run the update till today even I know that my iPhone runs current OS 9.2.1. Centainly I know that something is off - as apple has end to end programming. This must be fixed through syncing my iPhone to my iTunes.
Indeed, I successfully downloaded the new software, while my iphone was connected to the PC all the way through - software was extracted by itunes, then it starts to back up... till it says IT CAN NOT BACK UP AS MY IPHONE WAS DISCONNECTED. But iPhone is still visible in iTunes 😟
cables were not touch, iphone was on the table not being use during the process, cable is 100% healthy (3rd party but new)
Removed my iPhone, reconnect it again and I try to do the process again. and I receive same result.
I run the iOs diagnostics and sent it to apple. I wish it will be fixed.
PLEASE HELP.