The An Lushan Rebellion took place over a hundred years before the end of the Tang Dynasty. Though it weakened the dynasty considerably for many years, it may not be the best example of factionalism being responsible for the fall of a dynasty, as it's very removed in time from the fall. 

Factionalism was irrelevant compared to other factors

http://www.indiana.edu/~e232/Time1.html  See "Tang Dynasty" section under "Mid/Later-Imperial Era."

The An Lushan Rebellion took place over a hundred years before the end of the Tang Dynasty. Though it weakened the dynasty considerably for many years, it may not be the best example of factionalism being responsible for the fall of a dynasty, as it's very removed in time from the fall. 

http://www.quora.com/Has-factionalism-been-responsible-for-the-fall-of-Chinese-dynasties-as-the-Chinese-Communist-Party-has-claimed  

This diagram is a transcription of a Quora thread, to compare collaboration to independent answers. I chose this topic because it had a manageable scope and specific arguments. Of course, the arguments added to Quora were not created to be part of a collaboration so it would be possible to extend this diagram in various ways, now that it is put together as a collaboration. 

Factionalism was responsible for the fall of China's dynasties.

Factionalism was a factor in the fall of the Song Dynasty

China had a lower per capita income in 1950 than it did in 1000AD, and during almost all of that period it was ruled by a meritocracy selected by exam and raised by a process design to instill civic virtue. (source: Matt Ridley's The Rational Opitimist, citing a report from OECD or World Bank or some such source.) They had no interest in progress that might displace the status quo. When somebody had a new invention, they buried the invention and cut off his head, if he was lucky.

It's likely that many of the answers are truthful, but many, even the most information-filled ones, seem to lack citations. History Example 1: https://www.quora.com/Why-didnt-China-break-out-into-smaller-nations-and-remain-so-like-Europe-today-during-its-long-history-What-is-the-difference-between-the-two  Coincidentally also about China, this topic has quite a few responses, some with large numbers of upvotes. The two top answers currently, https://www.quora.com/Why-didnt-China-break-out-into-smaller-nations-and-remain-so-like-Europe-today-during-its-long-history-What-is-the-difference-between-the-two/answer/Rohit-Patnaik-1  and https://www.quora.com/Why-didnt-China-break-out-into-smaller-nations-and-remain-so-like-Europe-today-during-its-long-history-What-is-the-difference-between-the-two/answer/Anthony-Tauro , apart from a few graphics, haven't cited their sources of information. History example 2: https://www.quora.com/Was-it-ever-possible-for-Germany-to-win-World-War-II  While a couple of the answers cite wikipedia, most make assertions without links to historical documents or otherwise. Looking at the History feed has similar results.

https://en.wikipedia.org/wiki/Song_dynasty#Northern_Song.2C_959.E2.80.931126  

"The reforms created political factions in the court. Wang Anshi's "New Policies Group" (Xin Fa), also known as the "Reformers", were opposed by the ministers in the "Conservative" faction led by the historian and Chancellor Sima Guang (1019–1086).[24] As one faction supplanted another in the majority position of the court ministers, it would demote rival officials and exile them to govern remote frontier regions of the empire.[23] One of the prominent victims of the political rivalry, the famous poet and statesman Su Shi (1037–1101), was jailed and eventually exiled for criticizing Wang's reforms.[23] While the central Song court remained politically divided and focused upon its internal affairs, alarming new events to the north in the Liao state finally came to its attention. The Jurchen, a subject tribe of the Liao, rebelled against them and formed their own state, the Jin dynasty (1115–1234).[25] The Song official Tong Guan (1054–1126) advised Emperor Huizong (1100–1125) to form an alliance with the Jurchens, and the joint military campaign under this Alliance Conducted at Sea toppled and completely conquered the Liao dynasty by 1125."