So do you think that the Zeng will eventually tank, say by the 1850s around?
Probably not.
Ultimately any theorizing that far in the future is a pointless exercise. Too much is up in the air still.
But my guess is it's more likely the 1900s. The Qing limped a long a great deal after their prime and they had it ROUGH. There's no reason to suppose that TTL China could have it worse and die earlier, given B444's preferred multi-polar world setting. But I can't reasonably see the Zeng Dynasty surviving into the 20th century if it has it better or the same as the OTL Qing. It's just too long for a Chinese dynasty to last.
Chinese dynasties since the earliest days are as follows: Han 400ish years, Jin 150, then lots of short lived dynasties which rarely unified China, then the Sui for like 40, Tang for almost 300, then a century of various unstable dynasties and kingdoms, then a good 300 odd years of Song, a century of Yuan, nearly 300 years of Ming, then another nearly 300 years of Qing.
It's like clockwork. The most successful dynasties rarely make it to 300, and tend to collapse under administrative pressure, corruption, and complacency before ever reaching that point. The Zeng unified China only recently, so unless they are like one of the short lived dynasties and only last a few decades (unlikely given they are far older than that as a dynasty of Southern China), they should last until about 1900 or a bit beyond now that they have the breathing room to get fat and lazy like every other preceding dynasty.