Mayan civilization is also wholly different in its decline, and stringing it together along with the rest (even stringing them all together) is rather silly, as most of the economic decline (particularly in the colonial powers) was a direct product of war debt and strain, or of natural disaster. An ultimate killer cannot be merely a symptom of something else.
Yes, this is very true. The Mayan civilization is one of the more peculiar in this world, in that it was no built on what we think of as inhabitable land. It was built in the middle of a swamp, whose waters were salty enough to be toxic to plant life. In fact, this is one of the exemplary cases for civilization evolving before or concurrently with domestication, as civilized people had to be around in order to render the land habitable: by spreading crushed limestone into the swampy pools, burying the salt and making the water drinkable. This created small isles of habitability throughout the Yucatan, with immensely fertile milpas, but the whole edifice was exceptionally fragile.
When Teotihuacan installed a puppet ruler on the throne of Mutal, this triggered war with Kaan. Kaan encircled Mutal in a ring of allied city states, and the wars, raging for over a hundred years, utterly demolished the Maya heartland. The land was no longer maintained, and it became uninhabitable; this was probably aggravated by drought; the only places Mayan civilization survived was to the north and south. The heartland utterly collapsed.
The Indus is again different, as legends and evidence suggests that widespread flooding may well have contributed to the demise of this civilization. Another environmental catastrophe, but also aggravated by the fact that other civilizations were encountering problems as well, and trade, which was the life-blood of Harappa, was declining. Thus, it was not so much a matter of Aryan invasion as that the Harappans fell apart, and their people intermixed with incoming Aryans who superimposed their beliefs on Harappan beliefs and formed the basis of Indian culture.
But I do think that you can string a common thread through most civilization collapses. Civilizations can always be restored after some collapse: look at China. Invaded by the Mongols; restored. Half the population lost to Black Death; restored. Manchu invasion; restored. This is not due to some inherent quality of the Chinese beyond that the people identified themselves as Chinese. This allowed them to maintain a longterm empire, where others didn't. In the end, what did in Rome was that people no longer really cared who ruled them. They accepted barbarian rule easily; it wasn't that important to them anymore. Chinese people have never identified as anything but Chinese, however. The conquests of Alexander may have Hellenized millions, but they still didn't consider themselves Greeks, so it fell apart. This also explains the easy rise and fall of steppe empires. Very few actually identified permanently with one group or another; the Mongols were able to absorb multiple other hordes into their own ranks. This is also why nation-states usually have such great stability: they are built on a single cultural unit. Since 1700, France still exists, despite trauma after trauma. The fall of the Ottomans meant the foundation of Turkey. The loss of successive German reichs only meant a new German republic each time. Russia, despite being shot, stabbed, poisoned, bludgeoned, and drowned to death, managed to survive repeated trips to the afterlife, much like Rasputin.
The point being that a nation only stops existing when people believe it stops existing... because what is a nation beyond a deceptive facade where people obey a ruler because they believe he has power?
EDIT: If the above seems incoherent, I'm busy with my NES and rather flubbled at staying up far later than my brain cells function for.