I've only found a Kraken twice in my current world; each time, after mining it a bit, it sank beneath the waves.
Will the Kraken eventually resurface in the spots where I originally found it? If so, what's the timer?
Or am I doomed to just sail around the world in hopes of finding a new random spawn?
21 Answer
These are known as "Leviathans" within the game, and colloquially, the term Kraken is also used. They have a chance to sink every time you strike one of the barnacles, and once they go under water, they never come back.
It's best to be prepared with several players spread out across the shell to coordinate mining all at once, and it's wise to bring a stamina potion and tasty mead, in case you end up in the water and have to swim back to your boat.
You can get more information on the wiki!