This paper deals with the so-called S-estimation, which is known to have up to 50% breakdown point and therefore yielding one of the most robust estimators against outlier values, in a multiple linear regression when the errors are dependent. We mainly focus on the case when these errors exhibit a long range dependence pattern.We establish asymptotic normality of the slope estimator via some maximal inequality results à la Wu (2003) for dependent data, more suitable here than Kim and Pollard (1990) ones used by Davies (1990) in the i.i.d. case.