It's worth keeping in mind that China's needs for military capability differed from the various Western empires.
Rome fought with Persia to the East, the Gauls and Vandals to the north, and Carthage to the south, as well as the colonised peoples of its own empire, pretty much constantly. As I understand history, China was buffered by land (north, west, and south), and sea (west) from any significant challengers. Most of its threats were internal, the notable exception being the Mongol invasions, but that wasn't until the 1200s BCE.
On the other hand, what China did have in absolute spades and wheelbarrows full was technology (including, for the record, wheelbarrows). I've only learnt of the major study of this myself in the past year, British biochemist Joseph Needham's absolutely epic Science and Civilisation in China. Needham conceived of the work whilst in China on behalf of the British government during WWII, and proposed a 5-6 volume treatment in the 1950s. Seven decades later the work continues, with the total volume count approaching 30. Author Simon Winchester tells the story of Needham in The Man who Loved China (a single volume, should you fear to ask -- not a foregone conclusion as several digests of S&CIC run to multiple volumes themselves).
The breadth, scope, and precociousness of China's explorations in science, maths, and technology are staggering. The volume listing of the work itself gives some sense of the scope and scale, this is given at Wikipedia: https://en.m.wikipedia.org/wiki/Science_and_Civilisation_in_...
Scientific thought. Maths, astronomy, & geology. Physics. Mechanical engineering. Civil and nautical engineering. Paper and printing. Spagyrical discovery (alchemy and immortality). Military technology. Textiles. Ferrous metallurgy. Ceramics. Mining. Botany. Agriculture. Agroindustry & Forestry. Biology & botany. Fermentation & food science. Medicine. Language and logic. Two volumes, topics unspecified, are given as "work in progress", I suspect these would concern military and weaving technologies respectively.
My knowledge of ancient Chinese history is fuzzy, but the Jin dynasty, the Song dynasty, and the Ming dynasty were all ended by the conquest of what the Chinese considered barbarians, and I seem to recall that barbarian problems (or at least the cost of barbarian pacification efforts) fueled the fall of the Han and Tang dynasties as well.
It's worth first pointing out that the timeline of that series is slightly misleading; for proper comparisons, you're not comparing the Han dynasty against Rome but rather the various Chinese dynasties against Western tradition from ancient Greece and Rome, through the Islamic and medieval worlds up to perhaps the end of the Early Modern, which does reduce some of the impressiveness of the achievements. It's also interesting to look at what the Chinese don't invent--they invented gunpowder, but neither corned gunpowder nor the arquebus; they never appear to have been much interested in geodesy or cottoned on to the idea of the spherical Earth; they developed printing, movable type, and paper but never developed the printing press nor the literary industry of Western Europe.
My Chinese history ain't so sharp either, but checking, the three dynastic periods you're referencing start about 1115, or some 700 years after the fall of the Western Roman Empire. The barbarian invaders in each case are the Mongols, whom I'd mentioned (along with the timeframe) above. So this largely proves my poiont.
Whilst yes, there are multiple Chinese dynasties being considered here, there's pretty much a single cultural tradition, as opposed to the equivalent period of Western history which spans Egypt, the Phoenecians (or Phillistines, from which Palistine comes from), Minoans, Greeks, Macedonians, and Romans, as well as the Persian, Syrian, and several other cultures from what's now considered the Middle East.
The whole quesition of why China's progress stopped where, when, and how it did is a fascinating one. It's actually what Joseph Needham was getting at, and is termed "the Needham Question". It's strongly related to the parallel question: why did the Industrial Revolution emerge in 19th century England, and not elsewhere, or earlier, or later? I've been exploring that and could venture some suggestions.
In aaddition to Needham, there are Karl Polanyi (The Great Transformation), Kenneth Boulding (The Meaning of the Twentieth Century), Jared Diamond (Guns, Germs, and Steel) and many of the titles in the series the Princeton economic history of the world (http://www.worldcat.org/search?qt=hotseries&q=se%3A"Princeto...).
Vaclav Smil's Energy in World History explores the question somewhat, though I'd suggest mining the excellent bibliography for further reading (I've got a scanned copy that's not handy for extracting refs at the moment). http://www.worldcat.org/title/energy-in-world-history/oclc/3...
I can see a few influences, some of which are pretty well developed by others, some perhaps not. Geography, politics, trade, uniformity, writing system, philosophy and theology, population, and environment all quite probably play significant roles.
Rome fought with Persia to the East, the Gauls and Vandals to the north, and Carthage to the south, as well as the colonised peoples of its own empire, pretty much constantly. As I understand history, China was buffered by land (north, west, and south), and sea (west) from any significant challengers. Most of its threats were internal, the notable exception being the Mongol invasions, but that wasn't until the 1200s BCE.
On the other hand, what China did have in absolute spades and wheelbarrows full was technology (including, for the record, wheelbarrows). I've only learnt of the major study of this myself in the past year, British biochemist Joseph Needham's absolutely epic Science and Civilisation in China. Needham conceived of the work whilst in China on behalf of the British government during WWII, and proposed a 5-6 volume treatment in the 1950s. Seven decades later the work continues, with the total volume count approaching 30. Author Simon Winchester tells the story of Needham in The Man who Loved China (a single volume, should you fear to ask -- not a foregone conclusion as several digests of S&CIC run to multiple volumes themselves).
The breadth, scope, and precociousness of China's explorations in science, maths, and technology are staggering. The volume listing of the work itself gives some sense of the scope and scale, this is given at Wikipedia: https://en.m.wikipedia.org/wiki/Science_and_Civilisation_in_...
Scientific thought. Maths, astronomy, & geology. Physics. Mechanical engineering. Civil and nautical engineering. Paper and printing. Spagyrical discovery (alchemy and immortality). Military technology. Textiles. Ferrous metallurgy. Ceramics. Mining. Botany. Agriculture. Agroindustry & Forestry. Biology & botany. Fermentation & food science. Medicine. Language and logic. Two volumes, topics unspecified, are given as "work in progress", I suspect these would concern military and weaving technologies respectively.
http://www.nri.cam.ac.uk/science.html