The future of Africa's only continent-wide political forum hung in the balance tonight as a committee of leaders from 21 countries worked behind closed doors to fashion a compromise that would permit the Organization of African Unity to convene a summit here after two successive failures.

The meeting, which had been scheduled to begin this afternoon, was delayed indefinitely until the committee named by the outgoing OAU chairman, President Daniel arap Moi of Kenya, could resolve the issue of representation for the rebel Polisario movement of Western Sahara.

Conference sources told The Associated Press late tonight that the committee was deadlocked. Libyan Foreign Minister Abdul Ati Obeidi said it would resume its meetings Tuesday morning.

Last August, the first attempt to hold this 19th OAU summit failed to muster a quorum in the face of a boycott led by conservative states supporting Morocco, which claims the Western Sahara territory.

The failure of that meeting, which was to have been held in the Libyan capital of Tripoli, also blocked the ambitions of one of the Polisario's leading supporters, Col. Muammar Qaddafi, who as its host would by tradition have become chairman of the OAU.

Last November a second attempt to convene the summit, again in Tripoli, also fell through even though the Polisario agreed to stay away. This time Qaddafi, as host, opposed the seating of the Chad government led by Hissene Habre, who had recently routed Libya's ally, Goukouni Oueddei, in that country's prolonged civil war.

Now a third attempt at a summit is being made here in Addis Ababa, the seat of the OAU's secretariat. Failure to convene a meeting this time could signal the death knell not only of this pan-African body's credibility but of its very existence.

The member states' concern has been demonstrated by the arrival of 27 heads of state, including the Polisario's president, Mohammed Abdelaziz, and all but one or two delegations. But despite Moi's appeal for the member states to put African unity above national political concerns, their unyielding stances have resulted in a confusion of pre-summit bickering.

To make matters worse, the chairmanship question remains an issue here. Moi, who has been chairman since the last summit was held in Nairobi in June 1981, is reportedly eager to relinquish his responsibility, but an attempt to give the chairmanship to Ethiopia's Mengistu Haile Mariam, who as host would have been an obvious compromise choice, may not succeed.

Qaddafi, who arrived here unexpectedly Sunday night, apparently still is campaigning for the job. Many of the more conservative members would prefer not to see the controversial Libyan at the helm of the OAU but are willing to give way on this point for the sake of unity.

As chairman, Qaddafi would have little real authority but would become the titular spokesman for the continent.

The United States, which has no diplomatic relations with Libya, is treading gently on the issue. The Reagan administration was accused by Qaddafi of organizing the boycott that blocked the first Tripoli conference.

Now U.S. diplomats in Addis Ababa are standing quietly on the sidelines so as not to provide a target for further accusations. Their caution has been sharpened by an Ethiopian press campaign against "imperialist countries" purportedly trying to undermine the success of the conference.

One U.S. source said, "If anything goes wrong and there's any appearance of interfering, it would have serious effects on U.S.-Ethiopian relations."

U.S. relations with Ethiopia, once a staunch ally, have been tenuous since Col. Mengistu's government became a Soviet ally in 1978.

At the end of the day, the leaders continued their closed session in search of a compromise.

Conference insiders said several members are pushing a plan to give Qaddafi the OAU chairmanship in return for allowing Habre's Chad delegation to be seated and agreeing to put the Polisario issue on hold until the next summit meeting. Such a compromise would enable the OAU to emerge scathed but alive from the worst crisis in its 20-year history.