FOR ALMOST four years, independent counsel Lawrence Walsh has been pursuing his investigation of the Iran-contra scandal and prosecuting a number of individuals who were involved. The most prominent of these was Lt. Col. Oliver North, who was originally convicted on counts of aiding and abetting the obstruction of a congressional investigation, destroying documents and accepting a gratuity. Those convictions were a high point of the Walsh investigation, because although the jury acquitted Col. North on nine other counts, a major figure in the Iran-contra scandal had been found criminally responsible.

That accomplishment was erased last July when a panel of the U.S. Court of Appeals here vacated the North convictions and sent the case back to the trial court for a new inquiry, involving a congressional grant of immunity, that will be extremely difficult to carry out. The panel's opinion also cast doubt on the durability of another major conviction, that of Adm. John Poindexter, whose trial had followed that of Col. North. Mr. Walsh immediately sought a rehearing by the full appellate court, which turned him down yesterday. The prosecutor says he will almost certainly appeal for Supreme Court review.

These setbacks are no fault of Mr. Walsh or his extremely well-qualified team of prosecutors. They have been more than diligent in following every aspect of this case that might have criminal implications. The North convictions were undermined because Congress wanted to have it both ways. Legislators demanded a full-blown, nationally televised hearing. They forced Col. North, Adm. Poindexter and others to testify against their own interests, and they handed out grants of immunity that have hamstrung the prosecutors. Yet they expected criminal prosecutions to proceed without impediment. The court of appeals, however, has been adamant in insisting that those grants of immunity be interpreted broadly, and this presents a challenge to any prosecutor.

Mr. Walsh is right in seeking Supreme Court review of the North ruling, for Congress surely will want to reconsider its practices if the tough standard is upheld. After that case is concluded, though, he will have to consider whether any more remains to be done.

This investigation has been long and thorough. Most of the main figures in the scandal have been prosecuted, and eight, including Col. North, have been convicted or have pleaded guilty. Yet rumors persist that a new grand jury is continuing the investigation. Even the names of supposed targets have been leaked and published, and their reputations remain under a cloud.

Because the independent prosecutor is so powerful and so completely free of supervision and review, the probe could theoretically continue indefinitely. It would serve the public interest if Mr. Walsh -- insofar as it is possible consistent with the need for grand jury secrecy -- would clarify his intentions and set out his timetable for future actions.