People generally point to the "Centennialist" movement, based around the 100 year anniversary in the 1960s, as the beginning of the end. In this climate, with civil rights and dissent in the air, slavery and social issues took on a renewed significance. The prolific and popular Bruce Catton led this movement. The "Centennialist" term, of course, did not arise until later.
Parts of the "Lost Cause" narrative persist today in popular thought. A Pew Research poll taken in 2011 showed that a 48% plurality considered the main cause of the war to be states' rights, with 38% citing slavery.
Academics today like to tear down the Lost Cause, but one might consider that they are trying to publish or perish and thus push the earning potential of "Civil War memory" studies to the brink by artificially inflating the importance of the movement. As blogger Dimitri Rotov argues in the article above:
"Agitating against 'Lost Cause' historiography invites one into a fantasy struggle against a pretend school of thought invented out of scraps of writing and speech and then built into a menace. Centennialism dresses up as Don Quixote to tilt against this windmill while its real foes line up for hard jousting."
Most of the works that I'm familiar with on the ACW and the Antebellum period are more recent, ranging from David Potter's The Impending Crisis (1976) to William Freehling's two volumes of The Road to Disunion (1991, 2007). Other historians whose works I've read—Kenneth Stampp, William C. Davis, and several others—address the blatant problems with the Lost Cause mythos as well in ranging from the early 1950s into the 2000s. However, that doesn't give a proper outline of the historiography, which I'll provide briefly below.
It's with the revisionism of historians around the 1960s, by no coincidence around the time of the Civil Rights Movement, that the previous views which deflected away from slavery as the principal cause of the war came into question. The conflict thesis of Charles Beard and the legacy it left became the dominant theme in CW historiography after its proposition in 1927. It tended to focus on the economic dynamism of the period, the shifting of a balance of power from the southern agricultural society toward northern capitalism, in turn creating an inevitable conflict over policies irreconcilable with each other due to the conflicting nature of the two economies. The shift in power meant northern dominance in federal politics, to the increasing dismay of southerners, eventually culminating in secession. This remained popular through the fifties, while a new historiographical argument emerged in the 1930s and 1940s (with Avery Craven and James Randall) that tended to frame the war as inevitable just the same, but more the result of the replacement of the statesmen of the earlier period (Calhoun, Clay, Webster, etc.) with increasingly radical and less pragmatic/competent politicians unable to address crises in the context of emergent abolitionist fanaticism. Both of these schools came under serious criticism with the aforementioned Stampp in the 1950s and '60s, which also did away with the Dunning school that tended to emphasize the utter devastation the North wrought on the South during and in the wake of the war. David Potter's aforementioned work is moreover an instrumental look into the immediate causes of the war, and did an excellent job of demonstrating just how slavery dominated national politics right up until secession. Eric Foner in the 1980s was instrumental in the revision of the Dunning school thesis on Reconstruction as well, reviving the reputations of the Radical Republican faction, the policies of U. S. Grant as president, etc., and shifting blame for the ultimate failure of Reconstruction away from the otherwise significant and laudable achievements in Civil Rights legislation.
Elements of the old schools, including the Dunning and Beardian traditions, continue into today, though they are utterly rejected by a vast majority of expert academics and authors.