The major argument for keeping affirmative action is that it is still needed and still justified.
The original point of affirmative action was to make up for past discrimination. The idea was that discrimination was no longer legal but that, even so, past discrimination made it impossible for racial minorities to compete on an equal basis with white people. For this reason, the Supreme Court approved of affirmative action.
Some people argue that the effects of past discrimination, and perhaps even of present-day discrimination, are not gone. They argue that minorities are still disadvantaged either because of current (largely unconscious) discrimination or because of the impacts of the systematic legal discrimination that continued up to about 50 years ago. They argue that 50 years is not enough time to eradicate the impacts of that discrimination.
This argument holds that affirmative action must continue because there is still a need for it. We cannot simply assume that racism no longer matters and that minorities are truly playing on a level field with whites today.