Well, it was really the Cubans who defeated the SADF in Angola with the help of US oil companies. Cuban and Angolan forces defeated the SADF at the battle of Quito Cuanavale, which is also called the Stalingrad of Africa. The Angolan Civil War deserves its own game. Anyway, this was in 1988 and secret talks between the ANC and the South African government were fairly far along. The arms embargo was also starting to hurt the SADF's combat effectiveness, especially in the air where the South African Airforce had lost air superiority to Cuban MiG 21s. Strikes and civil unrest back in South Africa also tied down South African troops that could have intervened in various border conflicts. Basically, the SADF ran out of money, men, and equipment. After Quito Cuanavale, South Africa's government decided to start pulling out of Angola and Namibia.
Could the SADF have invaded neighboring countries after this point? In theory, yes. The SADF remained a highly effective and professional force. However, South African society was tired of decades of war by this point.
At the end of the day, Mandela pulled off nifty trick: in ending Apartheid and the border wars, he made South Africa the economic capital of Southern Africa. South African businessmen ranged across the continent setting up mining ventures just in time to sell minerals to an emerging China. South Africa also became an important force in ending devastating conflicts such as the two Congolese civil wars. A desegregated SANDF often forms the backbone of peace keeping missions across the continent (civil war is bad for business). Today, south African troops can be found as far afield as Sudan.
Cuba won the battle, South Africa won the future.