It is much more than losing face. Losing sovereignity in East Asian countries, where nationalism is hyper active, is an attack directly on national identity.
The Chinese government now will cease to exist if it yields to independence demands from any of the separationist region. The nationalistic education has been ingrained into society at large, something nobody dares to question.
"Patriotism cannot be our final spiritual shelter; my refuge is humanity. I will not buy glass for the price of diamonds, and I will never allow patriotism to triumph over humanity as long as I live."
By a Noble Laureate.