Scotch,
Did you just start using the auto-download feature like I did and I found out what your and my problem is. Do you keep resetting Safari? I replicated the problem and the problem is from reading the boards that when that box comes up iTunes is trying to recreate a cookie so that is can remember that it's signed in for automatic downloads.
When you keep resetting Safari your removing a cookie that iTunes keeps to remember that your logged in. It's not shutting off the auto-downloads its probably because you keep resetting Safari like me. I've even replicated the problem.
Try launching iTunes again without resetting Safari then go ahead and reset Safari and you'll notice that the box will come up again. The solution, if you wan't to stay logged into iTunes and use auto downloads so that when you purchase a song or movie on one device for it to transfer to your other devices you have to stay signed into iTunes.
The reason I never noticed this box come up is because I've always signed out of iTunes and i just starting using the iCloud and automatic download feature and since I no longer sign out of iTunes resetting Safari affects a cookie that iTunes keeps when it stays signed in therefore you and me are creating the problem ourselves. These guys were right! I know this from reading the boards and I've just tried to recreate the problem myself and that's what's doing it. So go ahead and do what I did and you'll see.
Launch iTunes while signed in an using automatic downloads (recheck the 3 boxes for music, apps & books) and you won't see this box. Once you reset Safari it will affect the iTunes cookie so that it won't remember your signed in (even though your are) that your sign in and the box will pop up right after resetting Safari. Like I said the reason I never noticed this is because I just started using the automatic download feature myself and always signed out so I never saw the box and to use that feature you have to stay signed in to iTunes store. By resetting Safari you also turning off iTunes. So go ahead and feel free to recheck those boxes again and stay signed into iTunes store.
If you use the private browsing feature to ask sites not to track you I don't know if this will affect iTunes or not because I haven't tried to recreate that problem yet but I'm going to test it. Hope this makes your feel better!
Just don't reset Safari! when your signed into iTunes and have automatic download boxes checked. If your signed out of iTunes all the time you would have never noticed this box like I didn't until I just started using the feature staying signed in. You have to stay signed into the iTunes store both on your iOS device and your computer for it to transfer from device to device.