Minor nitpick - the second siege of Vienna was in 1683, not '81.
Well…Let’s tackle a couple of things.
The Islamic ‘Golden Age’ is considered to have ended somewhere in the 10th-11th centuries, depending on how you want to look at/define it ( and it is probably best to look at it as a continuum, with numerous declines, but no definitive date for a break ). Basically it saw the collapse of a dominant central authority and the fracturing of the Pax Islamica ( i.e. contraction of Islamic rule and penetration by outside invasion ). The Crusades were only one small piece of this phenomena. Internally the central authority of the Caliphate lapsed. This was occasioned/accompanied by serious economic decline resulting from millenia of over-irrigation ( rising water tables causing salinized soils ) and desertification in Mesopotamia ( massive decline in the revenues that had been the economic engine of every major state from ancient Babylon right through the earlier Caliphate ) together with damage from the fourth fitna ( Islamic civil war ) and loss of outlying revenue as increasingly autonomous dynasties broke away on the periphery and ceased to remit much, if any, tax revenue. The later Abbasid dynasty was also unable to recover traction due to increasing praetorianization from the 9th century, as the private imported armies of elite Turkic horse-archers based in Samarra began dabbling in Caliphal succession. By the mid-10th century the Abbasid Caliphate was politically irrelevant.
The eruption of the nomadic Seljuq confederacy into the Near East in the 11th century, though it “saved” orthodox Sunnism from both the Shi’a keepers of the Abbasids ( the Buyid dynasty ) and encroaching enemies ( the Isma’ili Shi’a Fatimids most prominently ) and temporarily re-united a large chunk of Caliphal territory into a briefly powerful state, in the end just compounded the problem. Both the Seljuq eruption and the later Mongol eruption caused major demographic shifts and massively increased increased semi-nomadic pastoralism at the expense of agricultural production. Henceforth the military system in the region, at least until the later Ottoman period ( and in some areas, like Persia, into the early 20th century at least in part ), would be dominated by the levies raised from the mostly Turkic pastoralists, creating a constant tension for states between the need to accomodate both military resources and efficient revenue-producing regions ( urban and agricultural areas ). Revenue often lost out. Further the Seljuqs also entrenched the iqta system of tax-farming ( so-called “Islamic feudalism”, though the analogy is not exact ). Like feudalism/manoralism in Europe it was a good temporary solution to the problem of governance in the face declining revenue and central control, but in the end it only accelerated those trends. The 13th century Mongol invasion, in addition to accelerating the trend towards pastoralism probably also permanently damaged eastern Persia, destroying fragile and difficult to replace underground irrigation works ( which they were indifferent to replacing ). It is also worth noting that the Near East has been getting progressively drier for millenia, which didn’t help.
As noted this chaos ( including the impact of the Crusades, but hardly confined to them ) produced reactionary backlashes, as thinkers reacted to the visible decline by denouncing a presumed moral laxity. This was most marked in Iberia and North Africa as the extremely intolerant Berber-centered religious movements of the al-Mourabitun ( Almoravids ) and al-Muwahiddun ( Almohades ) replaced the semi-enlightened successor dynasties to the Umayyads.
All of the above contributed to a marked intellectual decline. Less revenue = less patronage. Praetorianized regimes are generally intellectually conservative regimes. Nomad-based military dynasties are less interested in intellectual achievement that urban, settled dynasties. Reactionary thinkers are often concerned only with very narrow definitions of education. Cultures that develop siege mentalities ( and have at the time a well-founded superiority complex ) are less open to stimulating outside influences.
Not that Islamic culture and intellectual thought came to a shrieking halt. Cultural efflorescenses can be seen all over the place as time progressed. But the same tensions were always in place - a vigorous state might re-establish central control over a wide area, pulling in substantial excess revenue and re-building crucial economic resources. But they were still often dependant on tax-farms and pastoral tribesmen to maintain their rule and as central control faltered, so often did intellectual achievement.
Spain went under. North Africa, India, Persia and Anatolia fractured into statelets. Egypt and Syria under the Mamluks was the dominant Islamic power from the 13th-15th centuries and was an exception to the pastoralist trend, as it relied on an imported military caste. It also controlled a major source of land revenues in the Nile, had an important sugar-refining and textile industry, and it dominated the overseas spice and luxury goods trade through the Red Sea and in partnership with Venice in the Mediterranean as overland routes ( the ‘Silk Road’ ) decayed. But it was government by controlled chaos, a constant parade of ever-shifting juntas usurping control from one another. Further it was hit hard by the Black Death in the mid-14th century - populations in Syria and Egypt dropped by 1/3 to 2/5 and unlike the similar devastation in Europe, there was no silver lining. In Europe there was not only a demographic decline, but a temporary demographic shift as urban populations and disrupted serfs fled to the wilderness, cleared forest and basically quickened a reclamation of “wastelands”. There were few similar wastelands worth reclaiming in the Middle East and available for Muslim peasants to flee and hide from fief-holders. As the Egyptian economic system was in essence an extractive one, feeding a parasitic military caste and geared to keep them in luxury, it has been argued ( by Abu-Lugod ) that it’s health was more closely tied to labor resources than its contemporaries. As population declined, the Mamluk caste resorted to ever-more exploitive methods of extracting revenue and basically strangled their own faltering economy. When Portugal outflanked them in the Indian Ocean in the late 15th/early 16th century, bottling up the Red Sea and destroying the Indian trade that they had become dependant on ( which incidentally also crippled Venice ), the state was basically undone and shortly was absorbed by the Ottomans.
The 15th, but even more significantly the 16th century, saw a ‘Muslim resurgence’ as three major states re-establish control over most of the central Islamic lands ( i.e. excluding the periphery of Southeat Asia and SubSaharan Africa ). The Mughuls in India, the Safavids in Persia, and the Ottomans eventually most everywhere else except the interior and southeast of Arabia and Morocco. Since we’re talking about the Arabs, I won’t address the first two, but the Ottoman Empire was obviously one of the world’s great dynastic states. Not only was it territorially huge and long-lived ( over 600 years ), but it saw a tremendous flowering of culture and even modernization in its early centuries. However as has been pointed out, the Ottomans declined and badly.
One crippling issue was the harem system. Earlier Sultans arose out of system where they held important posts before reaching the throne. After the mid-16th century this was not the case. Instead they emerged from cloister as often unevenly-educated political naifs, probably not the best system in the world for training the absolutist ruler of a massive empire. Absolute states depend on sound upper-management - absolutist France did well under workaholic, clever Loius XIV, not so well under Louis XV and Madame Pompadour.
The outflanking of the largely land-based Ottoman state ( to whom the Indian Ocean was at best a quaternary priority ) and Middle East generally by the Europeans, stifled long-term trading capacity and made them dependant on European monopolies. These would exert an increasing economic squeeze at the Ottoman’s expense as they declined, imposing ever more unequal trade treaties as time went on. The inflationary mess of the 16th century caused by New World silver hit the silver-standard Ottoman state even harder than Spain. Increasing court conservatism ( and the already made comparison to China is a good one ) led to not only ossification in the military system ( and concommitant praetorianization, which also compromised stable government ), but also retention of inefficient economic guild systems, that crippled innovation and entrepeneurship at the very time Europe was starting to take off. A general air of superiority ( again, at one time well-founded, just as with China ), and the antagonistic paradigm expressed in the tension between the Muslim and Christian empires led to a general stifling of cultural interchange, which was far more to the detriment of the slipping Ottomans. Long multi-decade wars on multiple fronts bled resources.
The point that the cultural center was Istanbul is also worth reiterating. The Ottomans conquered an Arab world already in decline as stated above and didn’t do much to regenerate it. It was treated as a revenue farm and otherwise partially left to languish. For example the Egyptian Mamluks were left in place and continued their parasitic, extractive ways. By the nadir of the Ottoman state in the 18th century, central control was almost negligible not only in most Arab regions, but in most of Turkish Anatolia as well and local governors looted the countryside as they pleased.
It is worth noting that the 19th century did see very significant reform and intellectual re-awakening in the Ottoman state. Modernization, in part impelled by the threat of the adventurer/rebellious vassal Muhammed Ali in Egypt ( and fr a time Syria, the Hijaz, and Iraq ), made significant strides. It is an open question how healthy a multi-ethnic Ottoman state would have continued to be if it hadn’t been dismantled after WW I. But it could scarcely been much worse than what did happen. Colonialism was less than healthy attitudinally for the MENA, fostering paranoia, humiliation, and resentment and generally not working to the greater benefit of the colonized ( though some clever dynasties worked it to their relative advantage, like the al-Sabah family of Kuwait ).
Anyway…what were we talking about 
? Oh, yeah - decline of Arab intellectual discourse from the classical period. A long, bumpy multi-symptomatic progression with numerous peaks, declines, and revivals. Dunno if I even answered the question fully, but the above is a start.
