Ancient Chinese history is quite cyclical, oscillating between unity and disunity. This has been quite a stable pattern ever since the First Qin Emperor unified China as an unitary state. Prior to this, China was ruled as a feudal state, similar to Europe during the Middle Ages.

In any case, notable periods in ancient Chinese history when China was politically fragmented - post-Qin Chu-Han Contention, post-Han Three Kingdoms, Wei-Jin Northern and Southern Dynasties and post-Tang Five Dynasties and Ten Kingdoms.

Contemporary China also saw a short-lived period of fragmentation in the aftermath of the 1911 Xinhai Revolution, with warlords carving up large swathes of land for themselves. Subsequently, Chiang Kai-shek succeeded with his Northern Expedition to nominally unify China under the Nanjing regime, even though many warlords still managed to preserve their local power bases.

I think historically, tensions have always existed between the central government and local governments in China. Due to the large geographical size of China, until recent advancements in telecommunication and transportation technology, it was largely unfeasible for the central government to exert effective control over all of China, and this left a large amount of autonomy for local governments to administer their respective jurisdictions with minimal intervention by the central government. Therefore, it is really not that difficult, practically speaking, for local governments to disavow the authority of the central government over themselves, especially when the interests of the local governments are no longer compatible with the interests of the central government. Nonetheless, China has been able to remain united for much of its history because of a deep-rooted belief in the idea of "unity under heaven", which has consistently served as a source of political legitimacy for many Chinese emperors.