Because of the reality of the US electoral process, Southerners would simply not be looking out for their own interests effectively if they formed their own party, rather than joining either the Democrats or the Republicans. Until the 1960's the Democratic Party largely did the bidding of Southern Democrats when it came to appropriations and civil rights legislation. Even today southern Senators often benefit from seniority within their party, which allows them to control key appropriations committees.
A national dixicrat party simply could not deliver as much for the south. They would have, in the best case scenario, something like 18 Senators, and 50 Congressmen. An impressive bloc, but one unable to pass its own legislation, except by logrolling with one of the major parties.