Hi Tegan,
I was also annoyed with this same problem recently. After I reformatted PC and added raid0 for my "C" drive....loaded iTunes....then out of the blue, it started prompting me for my password. It wasn't for the iCloud password like some people had. This one was for iTunes specific and in order to make it go away, I had to enter my password 3 X, every time. I'm pretty good with computers and software, but this iTunes thing was really p'ing me off !!!
I starting searching and came across this thread. Saw your post, followed the link....and VOILAAA it worked !!! YAAAAAY 🙂
Anyway, just wanted to say thanks and give you a big thumbs up.
Mike