IT IS BEING ASKED why Secretary of State Alexander Haig has invested so much of his time and the country's prestige in trying to help keep Argentina and Britain from coming to blows. The answer no doubt is that he had hoped to wrap up his mediation sooner, but the thing got stuck and he felt he had to stay with it a bit longer. That way may lie further embarrassment. But that way also may lie a break in the case. With the two fleets steaming toward a potential showdown in the South Atlantic, the opportunity for one or the other may be at hand.

The military situation does not seem propitious for either side. The British can dish out some impressive damage at sea, by most estimates, but the Argentines should still be able to cling to the islands they seized two weeks ago. The risk is that, deprived of the blue water that now separates their fleets, they will keep going at each other because they're there. The Security Council has demanded a cessation of hostilities--mostly an inhibition on the British since Argentina, being in possession of the disputed islands, has no reason to open fire. But the British could claim Argentina had ignored the council's first demand, for Argentine withdrawal.

There are other non-military pressures bearing on the two sides, especially, friends of international order will be pleased to note, on the Argentines. Buenos Aires, with weak reserves, needs every penny of its export earnings and its borrowings, and then some, to finance necessary imports and to keep up payments on its immense debts. The British have frozen Argentine assets, cut off trade and credit, and induced their European partners and Canada to bar Argentine imports. In return, Argentina has frozen British assets and suspended payments on its London debts. Britain's reputation as a safe financial haven has been shaken.

But Argentina appears to be much more vulnerable. If there are prudent people in the junta in Buenos Aires, they should be looking a month or two ahead, beyond the drama of the fleets, at the possible collapse of the economy and--if that happens--at the sure collapse of their own leadership. From a cheap triumph gained by illegitimate arms, they would have moved to political disaster. The way to avert it is to enable the Haig mission to succeed.