OP's question is related to a rather controversial topic in the areas of economic history and world history. The central issue of the so-called "Great Divergence" debate is as follows: Why did the Industrial Revolution happen in the West and not in China (or anywhere else)? The answer to this question largely depends on who you ask. I will summarize two of the major approaches (these are by no means the only theories regarding the rise of the West, for example the world-systems theory also has many proponents):

• Eurocentric school: This is oldest approach, dating back to Karl Marx and Max Weber, which has persevered through the work of historians like David Landes. Eurocentric historians attribute the Industrial Revolution to cultural, religious, or institutional qualities that are unique to Europe. Weber's view was that the "Protestant ethic" was crucial to the emergence of the Industrial Revolution. The West's "spirit of capitalism" could be explained by the Calvinist belief in predestination. Landes in his Wealth and Poverty of Nations also attributes the Industrial Revolution to the cultural values of the West. While he concedes that many technologies originated from China, he argued that China lacked Europe's culture of innovation and institutionalized property rights, which prevented China from industrializing.
• California School: This approach is more recent and has grown in response to the declining popularity of the Eurocentric approach in academia. The thesis of most California School historians is that both China and Western Europe were capable of industrializing, and that the rise of the West was neither inevitable nor permanent. In their view, Europe was less advanced than civilizations in Asia until a few centuries ago, when fortuitous circumstances in the West allowed it to surpass the East. Kenneth Pomeranz believes that prior to the Great Divergence around 1800, China and other parts of Asia were economically on par with Western Europe. In his The Great Divergence: China, Europe, and the Making of the Modern World, he attributes British industrialization to its easy access to coal and the resources it acquired through its colonies.

EDIT: Unfortunately, the majority of historians working on the Great Divergence have focused exclusively on the Qing dynasty. To quote Peer Vries (I would also recommend reading his article about the historiography of the Great Divergence):

The question why there was no breakthrough under the Song and why (probably) the Song achievement was never repeated is still open and, what is more surprising, all but ignored, by Californians as well. Debates about the Great Divergence almost exclusively focus on the question why Qing China did not take off. As I confine myself here to synthesising and evaluating existing scholarship, my references will also primarily be to the Qing era, although there are very good reasons in the future, pending further research to pay far more attention to the Song period.

However, Vries does cite a few historians who have examined the Song/Yuan period in relation to the Great Divergence. The first is Mark Elvin, who makes the case in The Pattern of the Chinese Past that Song and early Yuan China experienced a "medieval economic revolution" in agriculture,commerce, urbanization, and science and technology. Elvin attributes Chinese stagnation after the 1400s to what he calls the "high-level equilibrium trap". Chinese advancements in agricultural and transportation technology during the Song/Yuan period (in addition to inexpensive human labor and a large population) had reached the point that it discouraged investments into further technological innovation.

Eric Jones's The European Miracle also discusses the Song/Yuan period extensively. He writes, "By the fourteenth century AD, China had indeed achieved such a burst of technological and economic progress as to render suspect the frequently expressed belief that industrialisation was an improbable historical process." Jones gives two examples: a water-powered hemp-spinnging machine that is "as advanced as anything Europe until about 1700" and the Chinese production of iron in the 11th century, which was "approximately the same as the entire production of Europe in 1700." Jones attributes the rise of the West to a combination of several factors that were unique to Europe, but absent in Asia.

The answers in this old Askhistorians discussion based on a similar question by /u/astrogator don't really meet current standards, but you might find them a good starting point.

(This is a "follow up" question.) I see no mention of the portable clock. Is it an antiquated view that China refused adoption of the portable clock during one of their periods of general repulsion of all things Western? And that by not embracing it, organizing labor in an 'timely' manner was more difficult - thus leaving them at a relative industrial disadvantage?

Anybody care to answer OP's original question?