Okay, so I found the problem. It was a rather embarrassing oversight from my part...
In the previous mission, the player flies as Alpha 2. Alpha 1 gets blown up there (self-destruct). Because of that, I didn't add him in the red-alert mission. Which automatically makes the player Alpha 1. So, because of the red-alert, he doesn't have a ship. I decided not to have this particular mission a red-alert one; it's the easiest solution to the problem, and I think it will also improve playability.
I've attached a mini-campaign (well, technically it's a campaign, although you just have to sit back and watch) demonstrating the effect.
[attachment deleted by evil Tolwyn]