In my experience, checkpoints just won't save if you are in bad shape. I usually think there is a way out of the position of nearly any save, so it annoys me when the game decides I am not worth saving lol. This may be an Anniversary or even MCC thing though. In the coop when we worked out you could go back down the path before the ship to resave, it made all the difference. It's not obvious, but it is convenient!
The next part on the ship was the hardest of all so far in coop though, with the invisible elites with swords in close quarters, so annoying. We also got the messages about 0% marines saved and such ... and that's how it should be :).
This level is also where we learn the valuable lesson that this world has edges and they can be fallen off. It is the feature I dislike the most, when comparing to Marathon, especially in the multiplayer. It is hard enough work without so many not so obvious drops to death waiting for me. At least the SO could survive the fall!