This list suffers from a powerful recency bias, but of the dates listed (and probably of those not listed) I voted for 1862, which was arguably the last time when the U.S. could plausibly have ceased to exist.
Even if the Confederacy had won it is not like the rest of the United States would have broken up? The country would obviously be a lot different, but it is not like the US would cease to exist. If anything I'd say the last time the US could have ceased to exist was when it was fighting the war of independence (even the 1812 war was in self-defence from Canada's perspective and Britain had 0 interest in reconquering the US?)
The US would still exist to this day, with still most of their current territory (minus the confederacy obviously) and would have still been the number 1 superpower for much of the 20th century, though the Cold War would have been closer and I suppose China would have already beaten the US in terms of power at the turn of the century but the US would still be a comfortable number 2.
That all assumes history still goes through a similar path as we know beyond the Civil War of course which is a big stretch but still.
It really is. Taking it for granted that the U.S. would keep control of its OTL territory minus the eleven Confederate states is a dubious assumption at best. We know in reality that the Confederacy coveted the Southwest, while the border states (particularly Missouri) would have remained sharply divided. (It's not difficult to imagine St. Louis as a kind of North American Alsace-Lorraine.) Meanwhile, an independent South means the Midwest no longer has free access to the Gulf via the Mississippi River, with enormous implications for the post-war economy. In short, even if there were no more secessions after 1861 (a very big
if when one considers the many secessionist plots simmering in California and the Midwest), a Confederate victory would change the North American political and commercial landscape dramatically. Partisan politics would be similarly effected: without the Solid South, the Democracy would need to evolve to appeal to new constituencies, and it's likely "waving the bloody shirt" has a very different connotation ITTL. That's not even to mention the foreign policy implications: does a United States with a powerful, hostile neighbor on its Southern border (possibly with the diplomatic and/or military support of Britain and France) still pursue imperialism in the later nineteenth century; or does it instead focus on mustering its military and industrial strength for a reconquista? How does that impact WWI and beyond? (If the U.S. never acquires Hawai'i, do we still intervene in WWII, assuming there
is a WWII.)
All of this is counterfactual, obviously, but handwaving the breakup of the Union as a minor obstacle to the progress of history as we know it strikes me as frankly ignorant of what was actually at stake in 1862 and how the American Civil War differs from European separatist wars.