Yesterday I unlocked Ifrit HM and did it for the first times.

First try: <10 minute queue: Sadly a fail.
Second try: <10 minute queue: Succeeded, progressed story quest.
Third try: >20 minute queue: Cancelled queue because I would need to go 1h30 later.
Fourth try: >20 minute queue: And still counting right now

Does it matter that I completed it once? Does the duty finder put me in front of the queue if you need it for story quest?