I think the first thing you have to look at when answering this question is how exactly one defines the Silk Road. The most narrow definition would be the trade of Chinese silk overland through central Asia and onto Iran, India, the Levant and beyond. This image gives a reasonable illustration of this route. The broadest possible definition would also include major sea routes, and encompass many more good travelling in both directions, not just silk.

What is much more certain, however, is that Chinese trade with the outside world changed significantly during the 10th and 11th centuries. The overland export of silk had been the dominant route for Chinese goods heading west since the Han dynasty, around the 1st and 2nd centuries BC; this was gradually superceded by a maritime trade, primarily exporting porcelain, in the closing centuries of the Tang dynasty. There are multiple reasons for this, which I will try to explain in brief below.

1. Military defeats in the West

The route from China into central Asia passed through the Gansu corridor, and through the Tarim basin (in modern day Xinjiang). This important route had first been pacified by the Han dynasty, who subjugated the city-states of the Tarim basin, and helped protect the Gansu corridor routes from raids by the nomadic Xiongnu (and their successors) to the north. Chinese control of this strategic region was lost with the fall of the Han, and was not regained until the Tang Emperor Taizong lead a series of campaigns in the region in the second half of the seventh century.

The Tang were not able to hold onto the territory for long; they held it for only two decades before losing ground to the rising power of the Tibetan Empire. To the north, the Gökturk and later Uyghur Khaganates would also compete for influence in the region - although mostly as nominal allies of the Tang. To the West the Abbassid Caliphate was expanding in Central Asia, and also engaged militarily in the region. For the next century the four powers of Tibet, Tang, Abbasids, and Gökturks/Uyghurs would compete for control and influence of the Tarim Basin and its wealthy oasis towns. The Tang were eventually driven from the region in the middle of the eighth century. The An Lushan rebellion of 755-763 crippled the Tang militarily, and politically, putting a final end to Tang ambitions on the western regions.

The end of Tang military and cultural influence in the Tarim alone would likely not have ended the overland trade, but this was accompanied by a series of significant social and cultural changes that helped shift the focus of Chinese civilization from the West to the South and the East.

2. Decline of Buddhism in India and Central Asia

We are used to thinking of Buddhism as a very east-asian religion, but for much of its early history in China, Buddhism was seen as a foreign Indian faith. For Chinese Buddhists, India was seen as the heartland of the religion - something of a 'holy land'. Buddhist monks such as Fa Xian and Xuanzang had travelled great distances to study under Indian Buddhist masters, and to bring precious Buddhist texts back to China. Buddhist ritual items were traded by Indian and Sogdian merchants on the Silk Road in exchange for Chinese silks.

However, Indian Buddhism was already in a decline during the 7th century when Xuanzang visited India. As the faith lost ground in India to Hinduism and Islam, the authority of Indian Buddhist centers as the custodians of the faith began to wane. In China, indigenous schools of thought such as the Pure Land school and the Chan school (the predecessor of Japanese Zen Buddhism) began to supersede the teaching of Indian schools.

As China came increasingly to be seen as a Buddhist centre in its own right, the old religious trade links with India began to dry up. Chinese-made ritual ware, and Chinese-printed Buddhist texts replaced products imported over the Silk Road. Again, China began to look away from the west, and towards the emerging Buddhist sphere in East Asia.

3. Opening up of Southern China

One of the most significant prerequisites for a shift to maritime trade was the movement of people from the Northern China Plain into the southern regions. Whilst the Han had established commanderies in the far south, it was not until later that Chinese speaking people would settle in the region in large numbers. The first major movements came during the Northern and Southern Dynasties period, where non-Han peoples conquered large swathes of the North - pushing many Northern families to the south.

Agricultural advances under the Tang allowed larger areas of the mountainous south to be opened up to cultivation, bringing people south in ever increasing numbers. Vast infrastructure projects such as the Grand Canal were undertaken, to bring food from the ricebaskets of the south to the much drier lands around the capital Chang'an. On the back of this domestic network of trade new towns sprung up, bringing more people south, and stimulating the growth of a wealthy merchant class.

This influx of people to the South would open up new harbors on the South China Sea, particularly in the far South-East in modern day Fujian. These would become huge, bustling port cities - connecting China to a new network of international trade across the Indian Ocean, and the South China Sea.

4. Islamic Trade Routes

The Chinese were not traditional sea-farers, and it is only in the Song Dynasty that large Chinese merchant ships begin to make an appearance. The first maritime trade routes were pioneered by Persian traders - who were later overtaken by Arab traders in later centuries. Saffarid Persian sailors would ride the Winter monsoons across the Indian Ocean, to Malabar and Sri Lanka, where they would buy precious gems. They then rode the summer monsoons north to Malaysia, and beyond to the South China sea. Foreign merchants, mostly Persians and Arabs, settled in significant numbers in the southern cities (an Arab writer records that thousands of Arab traders were slaughtered in Panyu, modern-day Guangzhou, when the city was taken by rebels in 879).

Maritime trade had some significant advantages for China. Ships were able to carry huge quantities of relatively low-value products - making the large scale trade of porcelain viable for the first time. With the introduction of sericulture to the Middle East in the 10th century, China lost its monopoly on silk, and gradually the importance of this product was eclipsed by porcelain and other luxuries.

By the 11th century, China was tied into a huge international network of bulk trade. Chinese goods from the various provinces travelled south along the Grand Canal to the southern ports - from there they were traded for precious metals, spices, and exotic timber, and subsequently sold on along a network that spanned South-East Asia, India, the Persian Gulf, and East Africa.

Hopefully this gives you a clear outline of the changes that occured within Chinese trade during this period. I think there is room for debate about whether this was the end of the SIlk Road, or simply a new stage of it. Personally, I think the significantly different cultural and political enviroment that shaped/was shaped by this new maritime network is sufficient to call this a seperate phenomenon to the earlier overland trade.

I have not discussed in great detail the changes at the Western end of the silk road, or anything after the Song Dynasty, hopefully someone who knows these fields better than me can offer their input.

Most of the information here is drawn from Mark Lewis's overview of the Tang (Lewis, M. China's Cosmopolitan Empire : The Tang Dynasty Cambridge: Belknap, 2009.)

It was never stopped being used, however it degraded in terms of the economic potential of trade. After the end of the western Roman empire the trade with the orient was still being fueled by the silk road and important goods such as spices were imported from asia. Byzantium was the largest benefactor of this trade up to the time when its power degraded. After Byzantium became weak Turkey was the main direction for Europe to trade with Asia and Venice built its power and wealth thanks to being an intermediary in that trade. The demise of the silk road came along with the age of discovery and reorientation of the european trade from the eastern part of the Mediterranean Sea towards the Atlantic which started the decline of the Venetian empire and brought into being the raise of Spanish and Portugal empires along with the English and French later on.

If we define the Silk Road as a trade route mainly carrying silk from China to Europe, then the Byzantine Empire discovering how to produce silk themselves in Asia and Europe is what broke the economic viability of the Silk Road.

Procopius (the main Byzantine historian contemporary with the emperor Justininan) says that in 522 AD, two Nestorian monks who the emperor had sent to China to glean the secrets of silk production, returned with silkworm eggs hidden in bamboo canes. That was supposedly the start of Byzantine silk production.

The Arabs also learned how to produce silk, and spread it to Spain. Silk making spread from the Eastern Empire into Italy, and the city of Lucca became a center. When the Papacy moved to Avignon, silk producers moved there too, and silk production spread into France.

By the 16th century (after the fall of Byzantium) Lyon in France had become the center of European silk. The French Kings had granted Lyon a monopoly in France on silk production, and there were estimated to be 14,000 looms weaving silk in Lyon by the 17th century, with the silk industry employing 1/3 of the city's workers.

Source: http://en.wikipedia.org/wiki/History_of_silk

Many of the silk worms were raised in Provence, and this was a large industry in Provence until WWI.

Epidemic diseases hit European silkworm production in 1845. It was not until Louis Pasteur was brought in to help that by 1870 the disease began to be successfully combated. This epidemic, plus cheaper shipping from China through the Suez canal, plus the development of artificial fibers, reduced the importance of European silk production, and shifted back towards importation from China.

So, the Byzantines gained the secrets of silk production through industrial espionage, and silk production spread from there to other parts of Europe, where it remained an important industry until modern times. Production of silk in Europe, quite naturally, lowered the cost and made it uneconomic to transport it overland on a fraught and difficult journey from China.