Once you find her on the flight deck, DO NOT pull the beam out. Leave her while you search for a medkit. You'll find a medical stasis pod and a portable generator. Don't move her to it either, take it to her. Then when the option comes, keep powering the stasis pod, don't unplug it for the beacon, you'll find another one. If you do that and manage to keep Taylor alive through everything else, Captain Aya and Taylor will both survive.