Initially I was using "TIE Phantom:Whisper" w/Veteran Instincts and "TIE Advanced:Darth Vader" but I was able to reproduce several times with different loadouts. During combat phase, attack a target with Darth Vader. After the attack resolves, select Darth Vader again, select a target (same or different) and Darth Vader will perform another attack. I got the same result when using a swarm of "TIE Fighter:Academy Pilot". I believe the common element is when having 2 or more pilots of the same skill. As long as one has not yet performed an attack, the engine will permit the others to take another turn.

Unrelated bug: while testing the above I noticed that "TIE Adv. Prototype:Inquisitor" will treat targets in arc beyond range 3, as range 1, during the combat phase. Hope that helps.