The government of South Africa will survive this day -- the 10th anniversary of the Soweto uprising. But the means it has chosen to do so -- the most thoroughgoing repression in its history -- raises a far more fundamental question: Can South Africa survive this government?

President P. W. Botha's regime has run out of ideas, options and the necessary resolve to work out of its desperate situation. It may finally have run out of time as well.

For a long time, the government survived through the combination of black patience and white concessions that again and again turned out to be too little too late. But patience is an increasingly scarce commodity, and there is very little more to be delivered by way of cosmetic concessions. It is no longer, as the Rev. Allan Boesak said here nine days ago, a question of whether apartheid can be reformed or modernized or streamlined or beautified. "Apartheid," he told the annual dinner of TransAfrica, "can only be irrevocably eradicated."

For a long time, there were options for reform: local self-government of the townships, some sort of federation in which whites would share political power, an expansion of educational and economic rights to ease the transition to power sharing. But the options have evaporated.

Some Americans, startled recently by the antigovernment violence of the Afrikaner right wing, are now voicing sympathy for the Botha government, gripped as it is between the radicals of the right and the radicals of the left. Boesak said we shouldn't be "hoodwinked" into believing that the Nazi-like violence of the right forces new options on the government.

"What essentially is the difference between the right wing and the South African government? They are not fighting about the right of black people to participate in democratic elections; they are not fighting about the redistribution of the land; they are not fighting about the right of every black child to have a decent education; they are not fighting about issues of redistribution of the wealth of the country that we with our blood and sweat and tears have built up. They are not fighting about these crucial issues.

"So what are they fighting about? Nothing that matters to you or me."

The fight is over how best to maintain the power and privilege of white people. And that is also the point of the newly intensified repression designed to prevent today's commemoration of the 1976 Soweto demonstrations that ended in the death of some 500 blacks at the hands of the government.

The government hopes -- absurdly -- to forestall violence by preventing demonstrations and even church services on this bitter anniversary, by making arrests under special emergency laws, by jailing the black leadership.

The more likely outcome is to turn what might have been peaceful demonstrations into open warfare between blacks who are out of control because their leaders are in jail and whites who are out of control because the government has exhausted its moral authority.

Even if the government succeeded in limiting today's demonstrations, it wouldn't matter. The crucial fact is that the South African government is running out of time. And so is the American government.

President Reagan is still trying to nudge his South African counterpart into behaving more decently while it talks of reform. There was a time when that might have made sense.

The far more urgent question now is: What side is America on? Pretoria obviously thinks it knows the answer. It sees in the Reagan administration a sympathetic friend.

Boesak is convinced that it needn't be so, that President Reagan could, if he were to see the situation with sufficient clarity, save the South African government from its own folly.

"Virtually by lifting one finger, the United States can change the course of history in South Africa," said Boesak, now free on condition that he not discuss disinvestment. What could America do? "It can stop protecting South Africa every time the United Nations tries to do something, it could take our real leaders seriously -- not with meaningless words of moral indignation but with nonviolent pressure to push the South African government to the point where they understand that what is necessary is fundamental change."

Black South Africans will not easily or quickly win the war that is all but officially under way in that strife-torn land. But neither will white South Africans have peace so long as the Botha government remains in power.

South Africa, already out of options, is quickly running out of time as well.