What were the factors that led to Chinese political unification for much of its history, in contrast to India?

An early, powerful dynasty with an expert managerial vision set China on an early path to unification. Under Qin rule, languages, weights and measures, money, and legal systems were all standardized throughout much of China. This is an early example of the international relations theory of functionalism which roughly posits that regional integration in functional matters naturally leads to higher level political integration and connectivity.
In contrast to China, India never saw a period in which a single, all-powerful dynasty introduced the elements the Qin dynasty successfully introduced to China. Indian princes who saw military success in acquiring territory would also see these successes rolled back when their fortunes waned or reversed. Without functional connections creating permanent linkages, unification epochs in India became transient and dependent on inherently undependable factors such as military capabilities.
https://web.ics.purdue.edu/~rauhn/ancindia.htm

https://www.britannica.com/topic/Qin-dynasty

Many historians emphasize that, already in ancient times, China was very advanced in terms of the centralization of its government and the development of its bureaucracy. Often, they trace this progressive aspect of Chinese development to the climate and nature of the landmass. In order to survive in an area that had unpredictable rainfall and poor soil quality, the state had to command food as a resource and make the most of agriculture under very challenging conditions. Survival, particularly in the face of invasions from nomads from the north and civil war, necessitated large-scale irrigation projects and the ability to feed an army: tasks only a strong centralized state with the extensive bureaucracy could carry out. The Qin Dynasty's ability to achieve these goals was the secret to its rise and the creation of the first Chinese empire (221-206 B.C.). While there were numerous periods of fragmentation, effective rulers managed to bring about unification and extend the size of the empire following the basic recipe outlined above, and China continued to grow in territory into the modern period.
Interestingly, Indian fragmentation has also sometimes been attributed to its geography. India has numerous river systems and, resultingly, numerous urban centers with distinct cultures. The Indus River basin is the only path for foreign invasion. In a sense, the Indian subcontinent is a natural fortress. For this reason, the different centers could afford to remain fragmented, not having to unite in response to foreign aggression. At the same time, India has had periods of unity and centralization, with one example being the early Mughal period in the 1500s and 1600s.
http://www.chaos.umd.edu/history/imperial.html

https://worldview.stratfor.com/article/geopolitics-india-shifting-self-contained-world

In many ways this is a false contrast. Chinese civilization benefited from long periods of political stability. Some imperial dynasties were quite long-lived. The Han, Tang, and Song are good examples. And they depended on strong leadership, bureaucracy, and cultural and linguistic hegemony. But Chinese society was also marked by division and warfare. The so-called "warring states" period (475-221 BCE) is an example. This era of political chaos dominated by warlords also witnessed the development of lasting philosophical and spiritual ideas like Confucianism and Taoism.
India, in contrast, was not always divided. The Gupta Empire (ca. 300-600 CE) marked an Indian "golden age" of sorts. And there were other unified periods. The earlier Maurya Empire under Ashoka seems noteworthy. From the 13th or 14th century until independence in 1947 India was ruled, often loosely, by outsiders— first the Mughals and then the British.
India's richer cultural and linguistic diversity, and the deep contrasts in its environment, from the Himalayas in the north to the jungles of Kerala in the south, help explain why there was less political stability.
Anciently (i.e. before 2000 BCE), the Indus River Valley civilization was less unified than the early Yellow River Valley civilization, which came under imperial rule with the legendary "Yellow Emperor" Huangdi. This lack of political unity also perhaps explains the sudden disappearance of the old citadel cities of ancient India.
https://www.pewresearch.org/fact-tank/2013/07/18/the-most-and-least-culturally-diverse-countries-in-the-world/