How about a mission where you gamble your crew for a chance to win more crew? Storyline-wise it could be that you've discovered a ship (responded to distress call perhaps) that's been badly damaged and is listing in space. Scanners have detected survivors but actively burning plasma fires and decompressed decks present serious risk to any crew you would send over.

Each mission completion requires you to give up a crew member. What about these possible outcomes:
- Crew member is never heard from again (net crew -1) - 30%
- Crew member returns without any survivors (net crew 0) - 30%
- Crew member returns with a survivor from the damaged ship (net crew +1) 30%
- Crew member returns with two survivors (net crew +2) - 10% chance

If my math is correct that's roughly a 20% chance of gaining a crew member per completion. 90% of the time the players will break even, but every so often they'll hit the jackpot and gain 2 crew.

Maybe the final completion results in the rescue of a senior crew member with some special benefits.

That’s a great idea. What if we expand on it and make it a prototype ship, gone missing. Lets say we make the mission 10 or 20 times to complete a search and repeatable say 2 times or so. So upon finding this prototype vessel it marking and origins are human, but seem far more advanced than your own. Ship has been heavily damaged but still operational. Boarding party is required to investigate. You must choose who to send, time is limited, ship is unstable.
Now it’s only compliable 2 times for the purpose that it makes you have to decide what best suits you for the completion reward. Giving diversity in what is in the game and gives you the choice on how to specialize your ship.

1. Send an engineer for a chance to receive a reward in the energy compartment
2. Send a tactical officer a chance to receive a reward in the weapons field.
3. Send a helmsman for a chance he will locate defense system for your ship.
4. Send scientist for advancement in research or a planetary advancement.

All attempts have a chance to find survivors of any field. All attempts also have a chance your crew member will die from the ship becoming to unstable. As for the reward make it for example:
The Engineer Officer reward
1. Common reward energy cube.
2. Advanced reward a energy technology that’s 1 lv higher than you currently have.

Completion reward of some advanced technology, say a trans-dimensional conductor(secret research has lead us to a device that folds time into itself causing energy to recharge 5 sec faster.)

The Tactical officer reward would be.
1. Common reward artifacts that boost attack.
2. Advanced reward a weapon technology that’s 1 lv higher than you currently have.

Completion reward a trans-dimensional laser ( secret research has led us to develop a weapon the bypasses all shields know Causing say 20-50 damage bypassing the shields hitting hull directly.)

The Helmsman officer reward would be.
1. Common reward of defense boosting artifacts.
2. Advanced reward a defense technology that’s 1 lv higher than you currently have.

Completion reward a trans-dimensional shield (secret research has led us to develop a device that will phase the ship in and out of actual time and space resulting in a 5% defense reduction to damage.)

The science officer reward would be.
1. Common reward finding 500 rp in the data base to advance your research.
2. advanced reward a stealth technology that’s 1 lv higher than you currently have

Completion reward a trans-dimensional Extractor (secret research has led us to develop a device that can tap into other dimensions planet adding it resources to yours. Effect +1 to all resources on planet size 1)

The risks of doing this mission are as said above, loss of your crew member.
Reward system say 50% nothing 30% common 10% find crew 5% advanced reward 5% loss of crew.