Throughout China's history it has been both a big country and a collection of smaller nations. The current big country of China really only goes back to the 1940s. In the first half of the 20th century it was divided into various smaller parts. Despite being big in name, after the fall of the Qing it was run by various warlords and other political entities, none of whom actually had control of the region as a whole.

This is actually a pattern that has repeated itself at the end of nearly all the great dynasties as well; The regional pulls and various points of unrest lead to breaking apart the larger whole, and in some cases -- such as the Three Kingdoms period or the so-called Five Dynasties and Ten Kingdoms period -- it was very much split.

Even within the unified whole you do have certain cultural groups with varying degrees of cultural and political autonomy. Nominally places like Tibet and Ningxia are autonomous (though in practice just how much of their de jure autonomy is actually respected is up for debate), and places like Hong Kong which since 1997 is part of the People's Republic of China also have some (waning) political independence, but then you also have cultural regions which have varying degrees of self-identification as separate. The Wu culture found in the Yangtze Delta region is quite different, but it's not conceived as such by the local population much beyond the notions of architecture and food. The Hakka on the other hand, further south, have a much stronger sense of cultural independence, even though they are still ethnically Chinese (Han). Geography has played a large role in these conceptions for the past century, as Shanghai (Wu area) has been of much greater significance to the politics and culture of both modern China and modern Taiwan than the places where the Hakka have traditionally been living, and while a good number of the nation builders were themselves from Hakka background (Deng Xiaoping, for example), they adapted rather than pushing their own culture on the whole of the nation.

The biggest factor though is that in China's recent history, regionalism hasn't ever reached a point where it superseded nationalism. The sense of being Hakka has never been greater than the sense of being Chinese on a large enough scale to create any sort of successful Hakka separatist movements. Hong Xiuquan, the leader of the Taiping Rebellion, was himself also Hakka, but this background did not have any significant role in his rebellion which was instead more religiously framed. Through fostering this national-racial Chinese identity, Modern China has managed to build some semblance of large-scale stability, at least among the greater Han population, such that it's unlikely that we'll see the current political entity breaking into various smaller countries any time soon.