Wisdom is not enough, sometimes it takes time as well

Two people I know are in a dispute, there is probably some truth on both sides. There is probably exaggeration each way as well.  All I hear are two different perspectives on basically the same issue.  My job isn't to determine who is right and wrong, but rather to help both of them see the others perspective.
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 Problem is , each of them are so committed to their own side, neither will open up to the possibility of conciliation.   I have been one of those people myself.  I guess that experience should help me with the mediation but the fact I can see the errors of each of them,  is  no help to me in conveying the wisdom I believe I have to reach a peace,  except it is enough,  Its just the time frame is much to long.