iTunes asks for password 3 consecutive times

Whenever I open iTunes, it gives a popup stating the session has expired and asks for my Apple ID password. The password has to be entered three consecutive times before it is accepted.

1. The password is not incorrect. The three prompts for password are identical: the session has expired. At no point does iTunes claim the password was rejected.

2. This happens every single time iTunes is launched, and it is always 3 times that the password has to be entered, no exceptions.

3. This happens regardless of whether iTunes is opening to my local library or the Store.

4. My iTunes library is stored on a Dropbox folder, which allows me to open iTunes from any computer I own (I have five Macs that access the library.) The password issue happens on all the computers, no exceptions.

5. All 5 Macs are running High Sierra.

My only guess is that the issue is related to the library not being stored in its default location, and I can totally see how the session is considered expired when opening the library from a different computer. What is annoying is that the password has to be entered three consecutive times. If it was just once, everything would make perfect sense.

Any ideas?