It has been over two years since the South Carolina Republican Party filed a federal lawsuit over whether the party can limit its primary to voters who identify with the party. The case is Greenville County Republican Party v State of South Carolina, 6:10-cv-1407. The case is far from being decided.
Back on August 2, 2011, a scheduling order provided that all briefs and discovery ought to be finished by June 15, 2012. But since then, the scheduling order has been revised several times. Currently, briefs and discovery are due by December 2012 and a trial is expected in January 2013.
Current law provides for an open primary for all parties that hold primaries. The Republican Party wants to exclude voters who are not sympathetic to the Republican Party.