Dark Depths has a state trigger. There are some special rules applying to those. First, a state trigger will go off when the game state matches its trigger condition. Second, it will not retrigger, even if the game state persists, so long as an instance of that state trigger is on the stack (to avoid building up an infinite stack with no way to resolve anything). But, third, the trigger will go off AGAIN, if the last instance of it is gone from the stack and the game state still matches the trigger condition with the source being in the appropriate zone. This means, that countering a state trigger without altering the game state to not match the trigger condition will simply result in it triggering again.

603.8. Some triggered abilities trigger when a game state (such as a player controlling no permanents of
a particular card type) is true, rather than triggering when an event occurs. These abilities trigger as
soon as the game state matches the condition. They’ll go onto the stack at the next available
opportunity. These are called state triggers. (Note that state triggers aren’t the same as state-based
actions.) A state-triggered ability doesn’t trigger again until the ability has resolved, has been
countered, or has otherwise left the stack. Then, if the object with the ability is still in the same zone
and the game state still matches its trigger condition, the ability will trigger again.