iTunes 12.1.2 keeps asking for my password!

Every time I open iTunes 12.1.2, it keeps asking for my password - no matter how many times I type it in! I have played with the cookies settings in Safari but no changes on my part effect the constant requests in iTunes for my password.

How can I stop these annoying pop-ups? From reading the support community's blogs, it seems that this has been going on for several years, but I didn't have this problem until this current version of iTunes and Yosemite.

What can I change to be rid of this problem?