I wouldn't say that it's impossible for a nation as big as and as populous as China to stay together. I mean, just look at the United States. Granted, the population is much less than China, but they're more or less the same size, have a generally uniform culture and national identity, and in the US' case, have large chunks of territory not connected by land (Alaska) to the heartland. Ditto for Russia.
However, to keep China united...difficult. IMO the biggest problem was the Qing's inability to modernize their nation and maintain centralized control back in the late 19th Century. Had they pulled a Meiji, it might have worked out, though admittedly Qing rule was on very shaky legs from the 1850s onward.