On my Macbook Pro, iTunes keeps giving me a "sign in to the iTunes Store" popup (over 50 times).
This is not a complete answer, but it does help.

In Preferences, disable any options that require access to the internet. That includes: General &gt; Grid view download badges and untick General &gt; Automatically retrieve CD track names from the internet; all options in Downloads and Store; and untick Advanced &gt; Automatically delete watched movies and TV shows.

After disabling all of these, the number of times the popup appears may fall from dozens and dozens to just 3.