My impression was that you wouldn't know what the situation that caused the problem was. Basically, it'd be like a sci-fi show (Star Trek type series) where the plot was 'ship broke down' every episode, only the reason changed. Sometimes it would be mynocs chewing on the power cables, sometimes it would be that they discovered and ancient monolith, sometimes it would be that they answered a distress beacon and found some wierd eggs, whatever.
I got a distinct 'multiple ships' feel, with a play something like spelunky. Each game would be unique, but there'd be a metagame that would encourage you to keep playing, whether Bob the space engineer died or not.
That being the case, you'd need multiple distress calls, and multiple unique root causes (chosen randomly) for each one. If it were me, I'd have multiple solution types (simple physics puzzle if it just broke down, little bit of FPS action if it was aliens, whatever.)as well. The key to keeping the tension high is making sure that the boring ones aren't to boring, or too often.
Personally, I'd think that a few standard ship designs would be cool too, so that the player would know going in, "This is an Alpha class mining ship, I know what that looks like", but the situation, layout, etc, would change based on the problem. (Say one of the problems is asteroid damage. All of a sudden, the challenge isn't to figure it out, it's to get through the ship to the guns, but the ship is damaged and dangerous.)
To clarify earlier though: Say asteroids were the problem. That's the physical problem, done. Why were the asteroids there? why did the ship go there? why weren't the guns on? That can be more interesting. OR say that the ship is dead because someone opened the airlock. Why did they do it? Simple depression, insanity, alien threat aversion, what?