The Apartheid (Afrikaans for "separateness") system of racial laws adopted as national policy starting in 1948 (same year Truman desegregated the US Army).  The white government of the country did the simple math and decided they would need apartheid to maintain control of the native population, which was much larger than the population of British and Dutch descendants.

As the disparity between the two populations grew, as civil rights movements in the US and elsewhere progressed, and while organizations such as the African National Congress and Inkatha Freedom Party became a direct threat to their hold on power, Apartheid policies became more strict, and enforcement of them more aggressive.  So a good way to put this is that Apartheid strategy evolved in direct proportion to the size of the native South African population and the threat the white government believed them to be.

What strategies did the South African government use to maintain apartheid policies?

Successive governments in South Africa adopted a number of strategies to maintain apartheid. The various strands were combined under the premiership of P.W. Botha to constitute what became known as the "total strategy." This was in response to what was perceived as a "total onslaught," a threat to South Africa's security from the Soviet Union. The ruling white minority detested the Soviet Union, seeing it as an agent of subversion due to its alliance with the ANC. In response, the government pursued a number of policies, both domestic and foreign, to keep apartheid in place and repel the alleged Soviet threat.

On the international stage, South Africa attempted to gain support for its anti-Soviet stance. South Africa occupied a key strategic position during the Cold War, and part of its total strategy played upon anti-communist fears in the West in an attempt to bolster its position. South Africa used the cover of the Cold War to carry out undercover operations designed to destabilize neighboring countries such as Angola and Mozambique. This was intended not only to allow South Africa to assert itself economically in the region, but also to undermine the support of neighboring states for the apartheid movement.

On the domestic front, Botha, in common with his predecessors, used force in cracking down on growing unrest among the black majority. The detention and execution of anti-apartheid activists gathered pace, further contributing to South Africa's international isolation as well as making it harder to pursue any political initiatives to keep apartheid in place. Nonetheless, Botha did attempt to protect apartheid by making minor political concessions, such as a proposed new constitution which would give certain ethnic groups—such as coloreds (a multi-racial ethnic group) and Indians—voting rights, but not the majority black population. Botha hoped that by granting votes to colored and Indian citizens, he would secure their loyalty to the apartheid regime, forming a tactical alliance with the ruling white minority to thwart the political aspirations of the black African majority.