From what I can tell, it seems that there is no solution at this time. Over four pages of reports on discussions.apple.com and it seems that iCloud is broken for notifications in this manner on iOS.
The people it affect most is married couples. Ha. One possible solution involves calling Apple support. If you read through you will see on Oct 17th the person who was having the issue got a call back from Apple and they reset their Apple account. Many people are complaining that the option to save isn't working right now, it is a bug, apparently.
You can try to call and see if that will work. Good luck.
Here is a resolution from the discussions thread.
Through iCloud.com -> Calendar -> Preferences -> Event Updates: the ability to
tick/untick "Email me shared calendar updates" seems to save now when I log out and > log back in (that setting never used to hold). I have now turned this off for my
partner and he no longer receives email notifications (although it does still appear > in the Invitations tray on the iPhone Calendar app which is annoying).
My partner and I also share Reminder lists (a grocery shopping one, jobs on our home > reno etc) and after the iOS6 update on our iPhone's we lost the ability to
share/unshare these lists. Through iCloud.com -> Reminders you can now hover to the > right of the list name and a share icon is revealed where you can share/unshare the > reminder list with someone. Since iOS6 we also started receiving email notifications > everytime something was added to a shared reminder list (ie. Tomatoes) which was
effing annoying. This seems to have stopped =)