A SOMBER American footnote must be appended to the case of the three South African political fugitives who on Saturday walked out of the British consulate in Durban, where they had enjoyed sanctuary for nearly a month, and were promptly detained without charges by the police. The three, and three others who remain in the British consulate, had found refuge there after leading a boycott of South Africa's new constitutional system.

A statement issued by the three still in British care said that their comrades had walked out to expose the South African government's disrespect for the rule of law. What the South African government obviously is intending to say is that, although a majority of Indians and Coloreds reject the new system and the black majority entirely rejects it, the regime means to hold fast. The three who are back in detention have bravely made their point.

The statement issued by the three still in the British consulate also included a harsh attack on the Reagan administration. This is our special concern. The United States had protested the earlier detention of the six fugitives, and the prospect -- for three of them now a reality -- of their further detention if they left the consulate. But last week, when lawyers for the six asked the United States and a few other Western governments for "sanctuary and every possible assistance," the American Embassy denied sanctuary on grounds that the customary standard of imminent physical peril had not been met.

In general, requests for sanctuary are extremely difficult for U.S. embassies, forcing them to choose between honoring the American tradition of humanitarianism and hospitality to political dissent and getting along with the host government and conducting business as usual. In this case, however, it is necessary to ask how the South African government interpreted the embassy's rejection of the request -- a rejection handed down after Pretoria had declared that U.S. assistance to the fugitives would amount to encouraging a criminal act. Did that rejection contribute to a calculation by the South African government that it could safely rearrest the fugitives without fear of an untoward official American reaction?

Actually it is not at all clear that last week the American Embassy needed to reply directly to the fugitives' request for sanctuary, since at that point the six were still in the British consulate. Saying no, however, and on the bureaucratic and lawyerish grounds cited, quite possibly conveyed a deadly impression of bowing to South African intimidation. Regardless of whether the South Africans took the American stance into account when they rearrested the three on Saturday, it was a wrong decision. What is the United States government now planning to do to secure their release?