What if Banshee's Veil offered...

After the spell shield is popped, grants 10% tenacity for the next 3 seconds.

One immunity every 40 secs is too minor and in any team-fights, it wouldn't make too much of a difference. The extra tenacity is added so the player has some form of sustained protection against additional CC, which can be improved if the player is building additional items such as mercury boots.