It won't trigger again while the ability is on the stack, but if the ability is countered and Dark Depths is still on the battlefield with no ice counters on it, it will trigger again immediately
its an edict effect at sorcery speed
There are some permutations that get a little weird Remand, for example, which kicks the spell back into the owners hand, and Delay, and Memory Lapse, which stop the card (and the mana your opponent invested in it and the opportunity for that card to have the impact they wanted) but dont necessarily get rid of it
While relatively unassuming compared to other creatures with initiative, it does have one ability that no other creature with initiative has: flying
SHOP: Building this Nami list
I've used derivatives of this quote with friends and co-workers who are unfamiliar with Magic and it always earns a chuckle