We generally use bare shafts to tune with, since there are no feathers to immediately correct the way the shaft comes off the bow. If the bare shaft comes off the bow with a nock left, it stays nock left, or gets worse, as it goes down range. With a fletched arrow, the feathers correct the nock left within a few yards, which makes it more difficult to identify the problem. Which is a long way of saying that if you only see the tail left on a 60 yard shot with a fletched arrow, it is unlikely to be caused by an arrow tuning problem, which would have corrected itself long before then. (BTW, a tail left would indicate that the shafts are too weak, not too stiff).
If you were shooting in a crosswind blowing to the left, you might see a tail left on a long shot as the wind would affect the fletched tail more than the front of the arrow. Or, the arrow might be about out of gas at 60 yards and lose some of the stability it had when it was moving faster. But I don't know anything you or the bow could do that would cause a tail left to appear at 60 yards that wasn't already there at 20.