My phone had been failing to wake up when being pulled off its charging dock since my upgrade to 9.2 so I did a restore last night, wherein I noticed that iTunes warned me that several apps that were on my phone were not successfully backed up to my iTunes and I'd run the risk of losing them when I did the restore.
Since I sync my phone constantly with my iTunes library I thought that this was clearly an error on the part of iTunes or at worst some random app that was on my phone that was now pulled from the App store.
When the restore completed, I noticed that several folders were missing apps that I had recently downloaded and upon checking they weren't in my iTunes app library even though I had synced the phone earlier that day.
That's when I googled "itunes sync not backing up apps" and found this (and other) threads detailing the issue.
From what I can tell, people have been told by Apple that this is to do with new "App Sliming" protocols. Here's what I did that got my syncing back up and running again in all of my subsequent testing.
Update your phone/iPad to the latest OS.
Update your iTunes to the latest version.
Under "Preferences" > Store make sure "Apps" is checked off on the auto download section.
On your account icon (the little head silhouette next to the search bar in the top right of iTunes) go to "purchases" and (mostly for the sake of monitoring/testing and if you don't have an innumerable amount of apps in the cloud, select the "download all" option to pull everything you have in the cloud down to your local storage. I know that this isn't a reasonable move for some of you, but going forward, if Apple IS in fact monkeying with their local backup protocol this is the best way to keep tabs on stuff, store everything you own local and track what isn't copying to local with the "sync" or "backup" feature.
Once everything is downloaded, you should have NOTHING in your "purchases" section in the cloud (because you've pulled it all down. It will repopulate there as/if you delete stuff from your local storage.
Once I did all of that, newly downloaded apps that I downloaded to my phone and iPad work fine with "sync" they transfer over to my local storage just fine, despite allegations that I see from other users in this and similar threads that Apple has phased out local backup via the Sync feature.
I'm going to keep checking the cloud "purchases" section under my account after each sync session to see what winds up there vs what transfers locally to my computer/iTunes.
I believe that this may have just been a functionality overlap with some new features between iOS 9.+ and iTunes 12.3.0.44. Backing up from iOS 9 to older versions of iTunes prior to 12.3.0.44 omitted some apps that had been flagged with "slimming" protocols.
In my subsequent tests after getting everything restored and updated I was unable to get any newly downloaded or updated apps to NOT sync locally or transfer over to my computer.
If any of my recommendations are redundant or unnecessary please feel free to point out what and explain clearly, in layman's terms for myself and anybody else reading this/experiencing this issue.
Hope that some of this helps! I'd be terribly upset if Apple somehow phased out the ability to back apps up locally via iTunes and required that you download everything from the cloud in order to maintain backups as that's several extra steps that I wouldn't want to keep up with. Doing weekly "syncs" with my devices is all but a ritual for me now and it has always served me well for quick restore sessions as needed.
Oh, BTW, restoring my device seems to have fixed my dock wake up issues too. 😉