Often the reason is that the faces in the lower part are smoothed, and in the upper part the edges are hidden but the faces are not smoothed. When you try selecting the surfaces, the smoothed area behaves like a single face while the unsmoothed bits sekect separately. Without seeing the actual model this is my guess.
personally, this raises my eyebrows. Sure, part of the ship’s line could be hidden, but this ? the bottom of a simple cylindre ?
do you, by any chance, have a “ground” active (I know, it should be more of a sea). By that I mean a plane that represent the level 0 ? either a physical one you added, or one in the style panel ?
Because here, in this case, it would explain why the profiles stops appearing, simply because technically, if your model is partly below this ground, it’s not “cut” by it, therefore no lines or profiles are actually created.