When Worf's family name and honor was restored in the episode Redemption and it was acknowledged by the Klingon High Council that Duras's father was the traitor who collaborated with the Romulans on the attack on the Khitomer outpost, not Worf's - why was the family of Duras not discommendated like it was done to Worf's family in Sins of the father?
The answer to your question appears to be towards the end of Sins of the Father, the summary gives you the gist but it's much better in the episode itself:
K'mpec says the Duras family was too powerful and to expose him would likely split the Empire and cause a civil war. In order to avoid that, they decided to use Mogh as a scapegoat, believing that Worf, since he was in Starfleet, would not challenge the judgment.
Though I would suspect that after the Civil War they would likely shame the family, but Worf handles that in the end the old fashioned way.
In addition to Jorge's answer: even though the male head of the clan of Duras was killed, the family had been a powerful influence in Klingon politics for a long time. Despite the truth being told, most likely many Klingons owed some degree of debt to the family, or shared some dirty secret with them that they did not want exposed. Therefore, even if the new council members themselves owed nothing to Duras, they would be worried about reprisals from Klingons who did, or about direct reprisals from the sisters who were still relatively powerful.