those examples don't really work. you have to look at the political institutions of these places. of course China's been around for thousands of years. in fact, more like billions. same with Europe. continents tend to outlast civilizations. but the power struggles throughout China, Europe and the Middle East through the last 1000 years or so have been relatively constant.
But what I meant was, that cultures and what is passed down remain preserved in a lot of ways. Yes there have been struggles and change of government, different phases, etc... but like for example traditional clothing, language, religion, etc are often still present, where it is more of a 'niche' historical thing, here.
Edit:
An example of what I consider a true 'fallen empire' would be more like Native Americans (even though they weren't really an empire). They were integrated into a vastly different society, and they still have 'nations' and their reservations, and their culture preserved, but as one nation on this continent, they are 'no more'... they are relegated to what bits of land our government has set aside for them.