Serious scholarship out of Baghdad largely stopped a good century and change before the Mongols sacked the place, and given the propensity of the famous scholars' contemporaries to call them apostates, it is somewhat debatable inhowfar the era could even be considered "Islamic" rather than "Arabic."
The Mongol invasion also only covered a limited area, and had no impact on, for instance, Al Andalus, whose multicultural and intellectually advancing era had ended a bit after 1000 AD, to be replaced by strict conservatism (whose intolerance drove Jews and Christians alike up north).
Tellingly, when the Ottomans eliminated the Byzantine Empire and took Constantinople, the flood of Greek refugees reaching Italy dramatically influenced art, literature and natural philosophy. When the Mongols eliminated the Abbasids and took Baghdad, absolutely nothing changed in Arabia, Egypt or Iberia.
And given the propensity of the crusades era near east to engage in destructive behaviour not meaningfully different from modern ISIS (Al Aziz, one of Saladin's sons, tried to destroy the pyramids for being unislamic; he failed, but he gave it a try; the attempt is visible on Menkaure's pyramid to this day), there is an argument to be made that the Mongols merely beat the Arabs to the punch. Like shooting someone suicidal before he can jump.