At the part where the drone is spawned for you to kill, it so happened another player was in the sector. Apparently, they engaged and destroyed the drone (there were 3 drones in the system when I looked at my radar). I of course, did not receive credit, though no other drone spawned. I aborted the mission, and completed it the next time around. Perhaps if the player on the mission does not complete the kill goal but the target is destroyed, spawn a new drone?