Derelict has quite some mission breaking glitches, that's right. Replayed the campaign a few weeks ago and noticed a good deal of them, especially because i used some alternative approaches to the missions, and it turned out you can break some missions simply by beeing too successful

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Anyway, i didn't encountered this problem with the Cypher. I've zipped again through that mission a few minutes ago to see if i can replicate this glitch you've encountered, but it again worked well for me. Is the Auriga concentrating all their beams on the Cypher? In my playthrough, the ship distributed its beam firepower evenly on the Cypher, the station and the cargo ship that was still alive, so the Cypher wasn't hit by all of the Aurigas' beams. Maybe it's a question of mission timing and the Cypher was on different positions in our respective playthroughs, and if the Cypher is too near to the Auriga if the latter jumps in, the Destroyer concentrates all firepower on the Cypher, thus killing it in one shot. Dunno.
Try out if it works with the cheats. Even with glitches Derelict is a truly great campaign, and coincidentally the very next mission after "Descent" is completely awesome

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If it really doesn't work, i could even send you my pilot file from Derelict so you can continue after this mission from the simulator.
Edit1: If the Cypher won't jump out if you make her invulnerable, and it isn't possible to time the cheat accurately enough, you could make her invulnerable, destroy all but one or two of the Aurigas main beams (easy with trebutchets and support ship) and than make the Cypher vulnerable again (using the same cheat again) - this way, the Auriga will probably hurt, but not kill the Cypher, and she'll jump out as soon as she has received enough damage - as she is supposed to.
Edit2: Totally forgot it, but you can skip missions if you die five times in a row. Just commit suicide a few times.