Here is a solution that I believe is working for me.
My issue has been that I have a script that runs every 6 hours, at login, and 5am everyday. It will push iTunes to perform a "Check for Available Downloads." I also have an email rule that looks for the "A new episode of...." subject email and will ask for the check. The objective is to not have to wait for downloads and always have my new content downloaded without me interacting.
Recently I will come to my iMac and find I have iTunes in the forefront asking for my AppleID information. It will have the ID prefilled, but the password needs to be verified.
I browsed may threads like this one, and it pointed me in a few directions that have thusfar proved useful.
First go to Safari, Preferences, and under Privacy Delete all Website data.
Second in Sarari Preferences, go to Passwords. Look for any entry you do not recognize and/or has an Apple rooted domain name. For example appleid.apple.com or store.apple.com. You can do 1 of two things: Click "show password" and verify the informaiton is correct for that domain - OR - REMOVE the entry.
What I found was Safari had remembered a few INCORRECTLY entered atttempts, as well as someone else's Apple ID that was entered and had been saved locally.
My theory is the prompt was not a BUG, but rather the unlucky fact the first remembered entry iTunes was trying to use for your Apple ID happened to be an incorrect one. So instead of trying other entries, it prompts. This is good because it could lead to locking you out of an account without ever the chance to enter and save the correct entry.
For those having this issue, give this ago and see if it helps. Thusfar, I did it, re-opened iTunes, did a check for downloads and it did not prompt me additionally for my AppleID. I was still signed in to the AppStore and iTunes store, and the computer was still authorized to the machine.