IT has been four months since former Carter administration official Gary Sick revived charges of subterranean dealings during the 1980 presidential race. His allegation that Ronald Reagan's campaign manager, William Casey, conspired with Iran to delay the release of American hostages until after the election rekindled a long-smoldering controversy.Mr. Sick laid out the evidence from years of probing and poking, causing us all to relive that strange episode when the hostages, imprisoned for 444 days, were released five minutes after Mr. Reagan was sworn in. The circumstances have always been suggestive, but the evidence of actual wrongdoing, after Sick's charges as before, remains highly circumstantial. We don't know enough to arrive at firm conclusions, and what we do know comes from questionable sources. So why pursue the matter, as the Democratic leadership in Congress has decided? The reflexive answer, from the other side of the aisle, is politics. The Democrats, it's asserted, are desperate to tar a Republican president gliding toward reelection next year. Certainly political motives are present, as they always are in the halls of Congress. The makeup of the investigating committees, for example, could provoke a burst of partisan infighting. But politics alone can't explain the decision made by House Speaker Thomas Foley and Senate majority leader George Mitchell. The Democrats stand to take a lot of flak if this probe fails to unearth much more than we already know. And the chances are good that it might prove futile. The prime witness, Mr. Casey, is deceased, and the Iranians aren't likely to cooperate. Beyond that, the charges leveled by Sick and others assume an almost incredible cynicism on the part of the supposed perpetrators. Could American party politics really sink to acts that would prolong the suffering of captive countrymen and subvert the lawful conduct of foreign policy? That question, in itself, is why the investigation has to proceed. Its implications for the country's political health are too serious to ignore. The people need an answer, and Congress has a responsibility to seek one, elusive as it may be.