About 20 years at maximum, and this only if the South has a larger pocket of pro-Confederates in regions like the Ozarks and West Virginia then what existed IOTL. The kind of long guerrilla war that would result would be very geographically limited and would not have sufficient range to impair US military control of the entire South.
Guerrilla tactics don't work on more flat areas, and if guerrillas try to fight real armies they'll get their asses handed to them every time they do. *The* major long-term result may actually limit the Lost Cause's power in those parts of the South as people there will hardly remember with great fondness a regime that kept the region in turmoil and set it back several decades by so doing.
In the ATL Sherman, Sheridan, and Wilson will be seen by the North as even bigger heroes than IOTL.