In my last two missions (both needing 4 crewship kills) we had to abort the mission because at 3/4, there were no more crew ships to kill.
Mission 1: Saturn Proxima (can't remember mission; first one I think)
I was not the host. I killed a crewship with the forward artillery, but the kill was not counted in the tally - so we killed 4 crewships, but the game only registered 3. At that point, it became impossible to complete the mission -- we refined what we could and aborted the mission.
Mission 2: Earth Proxima (shipkiller mission)
We completed the fighter kills and shipkiller kills; but after searching the mission area it appeared only 3 crewships spawned in and we needed 4. I was host; when the team aborted, I could not. I couldn't access the menu at all, and had to force-close the game to get out of the mission.
Suggest that the missions spawn crewships until the game registerd enough kills - yes, it's harder, but as soon as you get the limit, any other ships can cut and run.