It's actually the opposite. The longer an arrow is in the air the more stable it becomes, until it slows down significantly. Inside of 10 yards the arrow is still trying to stabilize depending on how well the bow is tuned and the fletchings you pick. Most should be pretty stable by 10 yards though. The only thing that is really going to effect the arrow longer yardages is wind drift. And that is going to be depend on other variables besides time in flight.
I would really like to see someone prove to me that power stroke effects forgiveness. Let the bow get triggered by remote and have someone try to mess up the shot. The arrow will be in the target before they figured out it was gone. Of all the thigs that can effect forgiveness I would put power stroke and brace height pretty much at the bottom of my list. Right above lining the fletchings up with your blades probably

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Paul