@Pythagorean,
It's a book review, not a study of the subject, but it's a good link and sheds light on some of the big questions. Islamic science clearly continued past the 12th century, though, and there's an abundance of evidence for that. It was closer to the 15th and 16th centuries that it really slowed down, i.e. by the time that the huge Abassid and Umayyad states had collapsed. It's hard to call it a siesta any more so than ancient Egypt or ancient Rome took a siesta, because the whole civilization was a shell of its former self.
What's clear when looking at not just history but also the transfer of knowledge from place to place is that the rise in European science was contemporaneous with the rise in other parts of European society, and this was contemporaneous with (and closely related to) the decline in Islamic society and Islamic scholarship. The rise in European scholarship and science began in the 16th century and then exploded in the 17th century. But this was after a thorough exchange of ideas between these two spheres had happened for centuries at their frontiers: where Muslim Spain met France, where Muslim Sicily and southern Italy met the north, in the Mediterranean trade, and particularly in Anatolia and the Levant during the Crusades.
The major casualty of the Crusades was the Byzantine empire, and this was at the hands of Turks -- indigenous anatolians,
not Arabs. By the end of the Crusades and in the next couple centuries, the Abassids had been marginalized by the the Crusaders, by the Mongols, and by the Seljuk Turks. (There is even some soft evidence that the Mongols and the Crusaders had made an alliance against the Islamic world).