Is it necessary to repeat the ritual bath (ghusl) if a brown discharge appears after seeing the white discharge (al-Qassah al-Bayda’) and performing ghusl?

So long as you have seen the sign of purity (the white discharge), then you are pure. The brownish discharge that came down after it is of no consequence, due to the Hadith of Umm Atiyyah who said: "We did not consider the brownish or yellowish discharge after purity as anything."