How could developments that led to the expansion of civilization also lead to its decline?

We can think of a civilization like a business. If it expands too quickly without properly examining whether it can sustain itself in new markets, then it may quickly crash. Historically, civilizations that have spread very rapidly through military conquests later found that they had a difficult time holding on to these areas. In many ways it is like a company that experiences rapid growth and moves into new areas only for a lack of demand and poor logistics to end up breaking it. Empires from the Mongols to the Greeks made huge land conquests but then had trouble establishing political institutions to govern those conquests. As their armies left, those conquered areas quickly regained their own power.
Another way civilizations can decline is through maltreatment of their conquered subjects. When Hernan Cortes arrived in Mexico, he had an army of around 500 soldiers. Yet, he managed to conquer the mighty Aztec empire. How was this possible? The Aztecs were ruthless toward neighboring tribes and kingdoms, using them for slave labor and sacrificial victims. When Cortes arrived, the Aztecs' rivals and those that suffered under them joined in his conquest. The former Soviet Union was somewhat similar when it eventually collapsed (although much less bloody). Its strong-arm tactics against its satellite republics meant that there was no reason for them to stick by once the Soviet collapse was imminent.
Another way is through an inability to maintain a frontier when faced with economic instability brought on by climate change. The kingdom of Angkor in Cambodia may have suffered this fate, as did the Anasazi of the southwestern US. Drought may have affected both those kingdoms' ability to maintain their agricultural yields, which eventually led to a decline in wealth. As the kingdoms could no longer feed a standing army, those peasants on the periphery would have no reason to continue to submit their harvests (which were a form of taxation). This compounded the problem, making the periphery close further in as peasants simply moved outside of the sphere of influence of the center.
I would recommend reading the following book by Jared Diamond who covers this concept in detail.
Reference:
Diamond, Jared. 1997. Guns, Germs, and Steel: The Fates of Human Societies. New York: W. W. Norton.