I find this to be quite OP. With this card, a Dim shield essentially lasts 1 turn, and any other perm lasts 3 turns. It's a decent idea for soft PC, but it's a bit strong as a repeatable action IMO. In comparison, deflag costs 1 more quanta to destroy the permanent in 1-2 less turns, but it is not reusable.
Anyway, how would this work with Bone wall, Pillars/Pends, or Shard (or any other stacking perm i'm forgetting)?
@Jocko: A counter is the number of turns the perm has left, like Dim shield or Sundial's number.