I have been keeping in touch with this thread since Skiziks launched it several moons ago, and I have tried all suggestions with no firm solution reached.
Around mid-December I filed a bug report on the Apple ADC Developer site, followed by a nudge in late-January to advise that iTunes 10.5.3 had not corrected the issue. I have seen no sign of activity since the original report but I'm conscious that this is not a life-threatening issue!
This evening I filed the following update:
25-Feb-2012 07:05 PM:
Title: Repeating password requests when opening iTunes.
A number of users continue to report frustrations regarding this issue through the Apple community forum.
I have delved again into the issue and wish to append with the following:
1) Clear Safari of 'Cookies and other website data'.
2) Open iTunes. Will request for password at least twice.
3) Filename: Cookies.binarycookies at User/YourName/Library/Cookies will have been modified and Safari will now show the 'apple.com' cookie in the 'Cookies and other website data' list.
NB. Cookies.binarycookies will have increased in file size however the document content viewed with TextEdit will remain the same; just the word 'cook'.
4) iTunes can now be opened and closed repeatedly without any further request for password.
5) Close iTunes.
6) Clear Safari of 'Cookies and other website data'.
7) Open iTunes. Will request for password at least twice.
8) Anomaly is 100% replicable as previously stated.
Resolve: Is it possible for iTunes to store the 'apple.com' cookie elsewhere?
I would be grateful if other Mac users would check this out on their machines and report back. It would also be interesting if the Windows users who are following this thread could test this with their counterpart cookie files.