Gladiator War of Attrition on Bosses with Phases (Invuln)

Hello, would just like to ask about how this skill interacts with bosses with phases. Is this a stacking debuff that increments on the mob and will stay on them even as they disappear for their phase attacks/Phasing?(Exarch,Eater,Shaper, Aul, Liches etc).
For Maven it seems like it would be reset since she kind of dies(HP goes 0), but does it stay on the brain?

I think it does persist on, because the wording "ever been in your Presence".