A permanent with a stun counter that would become untapped instead stays tapped and removes one stun counter. Multiple stun counters can therefore keep a permanent locked down across several untap attempts.
Hylda of the Icy Crown rewards you whenever you tap an untapped creature an opponent controls, making her a natural fit alongside stun-counter effects. Proliferate can also add more stun counters to permanents that already have them, extending how long they remain frozen.
