When the first board rotted out and was replaced, that board became part of the ship through time. It might stick out a bit, look like "the new board," but by contributing to the whole of the ship, it became part of the ship.

This process repeated every time a board rotted out and was replaced; the replacement boards, by acting to keep the entire construct afloat, became subsumed into the whole that was the ship.

The ship is more than the sum of its parts, the boards and nails, rigging and cloth. One would have to deconstruct the ship entirely and rebuild it with all-new materials for it to no longer be the same ship.