I don't think the existance of Islamic Golden Age is in doubt, In essence it was a scientific and technological renaissance promoted by powerful leaders, maybe for their own good (medicine, astrology) but later gave a great deal to the wider scientific world. The origins have been recognised as coming from ancient Greek sources, who the Islamic scholars acknowledged and held in high esteem. That such outside esoterica was accepted within Islamic circles has to point to fairly open-minded leadership. To me this contradicts what I've understood about Islam generally. Certainly there was continiual opposition to the dissemination of foreign treatises from within, for instance al-Ghazali who "repeatedly warned against exposing Muslims to potentially misleading though essentially innocuous rational science" (p.183 The World of Islam ed. Bernard LewisT&H 92)
There does seem to be some doubt over how long the Golden Age lasted and what ultimately caused its demise.
As for the latter, there were external causes, like the Mongol invasion, but others see factors within the religion itself. Less open-minded governance saw a return to fundamentalism, rejecting rational science as it conflicted with the literal word of God?
More strident commentry is easy to find on the net:
Another result of the religious dominance of Islamic culture is that even when education is undertaken in Islamic culture, the emphasis is too often centered on Islamic studies. The Islamic world devotes such a disproportionate amount of its education resources on the teaching of Islam that it acts like an anchor that impedes forward progress. Not only does the emphasis on religious study take away from the study of knowledge that might help advance the culture, but it has the additional pernicious effect of cementing Islam's grip on the culture. Muslim youth are inculcated into a relatively unshakable Islamic belief system that perpetuates itself into perpetuity. Many Muslims spend much of their time memorizing the Qur'an. Memorizing such Qur'anic verses as "slay the pagans wherever you find them" hardly prepares Muslims for an increasingly technical world. from
here.
I have no doubt that the West was influenced directly by Islamic Golden Age, especially the applied sciences. The works of al-Jazari's Automata and the Book of Knowledge of Ingenious Mechanical Devices were well ahead of Western technology. Somehow the West applied such learning, and maybe Islam failed to build on it.