From what I've read, a single lingua france from Spain to Central Asia, along with the rise of paper and Indian numerals, allowed for rapid and broad transmission of knowledge. Many historians worldwide have pinned 1258 and the fall of Baghdad, and the rise of independent Islamic powers, as the end of the Golden Age. Yet we don't claim that the Age ended with the rise of Ummayad Cordoba or Samanid Central Asia, those powers had their own concurrent enlightenments. It seems to me that the biggest shift came when Arabic was no longer the majority language in Spain and Persia eastwards.
Hi, sorry for the lateness of my response.
I would agree with 1258 as a solid end date for the Muslim Golden Age. While there had been deterioration in the political dominance of the caliphate for some time before that, you correctly point out that the ongoing rule of the Umayyads in al-Andalus doesn't point to that kind of "fall." It's really hard to overstate 1258 in the history of Islam.
While today many Muslims rightly point to the Crusades as an early example of Western/Christian anti-Muslim action, in her book The Crusades: Islamic Perspectives, Carole Hillenbrand points out that the Crusades did not play an enormous role in Muslim historiography until the colonial period, when it was an effective tool for understanding either colonial or postcolonial struggles. In fact Christians thought about the Crusades much more than Muslims ever did after they were over. The reason for this is that the Crusades were a drop in the pond compared to the disruption of the Mongol invasions. While the Crusaders won political control in the Levant, it was short-lived (less than a century for their first try at control of Jerusalem) or sporadic; while they held Acre until roughly 1291, their influence had diminished enormously. On the other hand, the Mongol siege of Baghdad struck at the heart of Muslim power and culture and crushed it under their heel. While there were conversions to Islam among Mongol rulers in the following period, it changed the face of the Muslim world forever.
A Franciscan named William of Rubruck once went to visit a Mongol ruler who was said to have converted to Christianity. In William's own account, the khan differed with him on this point. The khan said, no, you're a Christian; I'm just a Mongol who believes in Christ. In other words, the Mongols disrupted the traditional form of Islamic life. No longer were they the absolute political force that they had been (no matter what divisions among sectarian or political lines there might have been). Even the modes of thinking didn't apply anymore.
Now, many of those modes were functionally restored with the decay of the Mongol empire and the eventual rise of the Ottomans and the Safavids -- the Ottomans experienced their own sort of Golden Age, but we generally see it as distinct from the earlier, Umayyad/Abbasid one.
One reason for this, as you again rightly point out, is the difference of language. While Arabic texts were still important, the use of different languages in the Ottoman era distinguishes it from the earlier Arabic Golden Age. With that said, as important as the development of Arabic is to the "Golden Age," I'd rather see it as a symptom rather than a cause. Arabic grew in usage as the Muslim rulers consolidated power. It fell in usage after that power began to deteriorate, and finally, after that power was smashed by the great newcomers, the Mongols.