Bhishma Pitamaha was considered a very religious and righteous person in Mahabharata. Then why he did not stop Duryodhana? Instead he kept silent in Draupadi's Cheerharan.
Not that Bhishma did not Say anything, but yes he did not Do anything. He did not Do because of his oath of Seeing his father's image into the King who is the lord of Hastinapur. Had Dhritarashtra instructed him, he would have easily stopped this misdeed. But driven by blind love, Dhritarashtra allowed his son Duryodhana to conduct.
Now first of all let's get into the context of Sabha Parva when the Vastraharan event took place.
In the game of dice, with every move a player will loose whatever is kept on the stack. Yudhishtira after being lost himself in the game, at last put Draupadi on stack and lost it. With that all Paandavas + Draupadi became Slave / Das of Duryodhana.
However, Draupadi denied this concept citing that if Yudhishitra had already become slave/das then he automatically looses the right on her to be put on stack. This was a race condition.
Duryodhana & company were talking about technicality of the game and Draupadi, Vidura & Vikarna were talking about ethics. In other words former were seeing Duryodhana and Yudhishtira as just players and everything else as commodity. While latter were seeing them as brothers and everything else in view of family values.
When she asked this question in the assembly to all seniors,
Bhishma said, 'O blessed one, morality is subtle. I therefore am unable to duly decide this point that thou hast put, beholding that on the one hand one that hath no wealth cannot stake the wealth belonging to others, while on the other hand wives are always under the orders and at the disposal of their lords. Yudhishthira can abandon the whole world full of wealth, but he will never sacrifice morality. The son of Pandu hath said--'I am won.' Therefore, I am unable to decide this matter. Sakuni hath not his equal among men at dice-play. The son of Kunti still voluntarily staked with him. The illustrious Yudhishthira doth not himself regard that Sakuni hath played with him deceitfully. Therefore, I can not decide this point."
I feel whatever he said is quite correct even though it looks diplomatic. Keep ourselves in his shoes and ask to make a decision if the Draupadi was won fairly or not, the same answer will come: "Can't say for sure".
However, the dragging of Draupadi from her room till the assembly and disrobing her was entirely wrong. Because such humiliation is not dharmic even with the slaves or Das. Bhishma kept quite in that due to his oath, but he foresaw the upcoming total destruction and he did express it:
Draupadi said, '... Ye Kauravas, I am the wedded wife of king Yudhishthira the just, hailing from the same dynasty to which the King belonged. Tell me now if I am a serving-maid or otherwise. I will cheerfully accept your answer. This mean wretch, this destroyer of the name of the Kurus, is afflicting me hard. Ye Kauravas, I cannot bear it any longer. Ye kings, I desire ye to answer whether ye regard me as won or unwon. I will accept your verdict whatever it be.'
"Hearing these words, Bhishma answered, I have already said, O blessed one that the course of morality is subtle. Even the illustrious wise in this world fail to understand it always. What in this world a strong man calls morality is regarded as such by others, however otherwise it may really be; but what a weak man calls morality is scarcely regarded as such even if it be the highest morality. From the importance of the issue involved, from its intricacy and subtlety, I am unable to answer with certitude the question thou hast asked. However, it is certain that as all the Kurus have become the slaves of covetousness and folly, the destruction of this our race will happen on no distant date. O blessed one, the family into which thou hast been admitted as a daughter-in-law, is such that those who are born in it, however much they might be afflicted by calamities, never deviate from the paths of virtue and morality. O Princess of Panchala, this conduct of thine also, viz. that though sunk in distress, thou still easiest thy eyes on virtue and morality, is assuredly worthy of thee. These persons, Drona and others, of mature years and conversant with morality, sit heads downwards like men that are dead, with bodies from which life hath departed. It seemeth to me, however, that Yudhishthira is an authority on this question. It behoveth him to declare whether thou art won or not won."
Bhishma did not duck the question but he was really stuck between which to choose technicality vs ethics. That's were he made the mistake, because Dharma or morality was more on the ethics side than technicality of the game.