...where the prologue described how some critical military communication is ALMOST lost (in the real world, it was lost and found by the North), which results in military and political victory for the South.
The story takes place a generation later, when the second Civil War breaks out.
He follows this up with a 4-book series where the USA and the CSA are on different sides when World War One breaks out: the US is allies with Germany and Austria-Hungary, and the CS is with Great Britain, France, and Russia. The brutality of trench warfare is mirrored here as US troops invade Canada and the CSA.
Note: Turtledove wrote a stand-alone novel called "The Guns of the South", where in 2013 (or so) South African pro-apartheid forces use a stolen time machine to ship AK-47s to the Army of Northern Virginia. The time machine only goes back exactly 150 years, and the white South Africans decide that having a modern slave-holding nation would be in their interest to prevent anti-apartheid forces from integrating South Africa in the early 21st Century. I think he wrote it before the collapse of apartheid. Anyway, of course, the South is able to quickly overcome the North due to the increased firepower of their soldiers. This story isn't the lead-in to "How Few Remain", but it seems the research required to write this one triggered a new branch of "what if..." books from Turtledove that he wrote without the sci-fi element of time travel.