There was one day when the South could have lost. If McClellan had put his whole army in at Antietam, or attacked Lee in force on the second day, it could have all been over. But then, given that this is McClellan we're talking about here, it's not even a possible counterfactual.
I honestly believe that the South lost on April 12, 1861 when they fired on Sumter. It just took four years for them to realize that. I just can’t come up with a scenarion where they don’t win. The closest they could have come was if they had won at Antietam and the British did try to intervene and negotiate a settlement leading to Southern independence, but even then I think Lincoln could have survived foreign pressure and continue the war.