User blog comment:I Am Knowledge/Myosotis, The Flower of Chivalry/@comment-4434378-20120616025829/@comment-4490515-20120616191823

It procs whenever an ability hits an enemy, and refreshes if they're hit again. This way, she gets no sustain without expending mana.

The passive still gives her sustain, even without AP. AP merely helps her deal more damage with her autoattacks on marked targets, so it means she can still deal decent damage when spells are off cooldown.