It's hard to justify away the discovery of the Americas, since that development was the result of long term development of better shipmaking and navigational techniques that allow more ambitious voyages west.
Moreover, though, the universe itself was conspiring to destroy empires across the world; during the 17th century, you have dramatically less sunspot activity. Some years, we can get a hundred sunspots; between 1640 and 1710, there are fewer than a hundred. There's also increased volcanic activity, which means less sunlight reaches earth, and these temperature shifts lead to increases in El Niño activity; OTL, there was more than twice as much during the 17th century than today. It's not impossible for the dynasty to survive, but they'd need someone like Zeng Guofan to rise to the challenge, and their servants were found wanting in comparison.