It basically acts as a cooldown, so I don't see why it should not be affected by cooldown reductions, or maybe even Refresher.

The only thing which differs here is that it has 2 separate cooldowns, one for the evasion and one for the crit, so it could not made to use the traditional cooldown system. And cooldown reductions don't affect non-traditional cooldowns by default.

There are already several passive abilities which are affected as well, so it being a passive is not an argument for why it shouldn't be affected. Jinada, Moment of Courage and Entangling Claws (and old Tidebringer before it was turned active) are affected by reductions and resets.