The notification you are seeing is when iTunes decides to go to the ScreenCastsOnline feeds and check to see if there are any new episodes to download. The ScreenCastsOnline feeds are protected by a username and password (usually stored in your keychain) and if you are a valid member, the authentication box does not pop up.
If you are no longer a member, the stored username and password will not work, so the box pops up to allow you to re-enter the username and password, but of course, this will never work unless you become an active member again.
The frequency of how often the box pops up depends on your settings in iTunes, specifically the "Check for new episodes" setting.
To prevent the box appearing, you should "Unsubscribe" from the ScreenCastsOnline podcasts if you are no longer a member.
To do this, ctrl or right click on the Podcast title in iTunes and select "Unsubscribe Podcast"
You'll need to do this for all your ScreenCastsOnline podcasts.