Sitting recently on the dais on one of the periodic U.N.-sponsored conferences that his position dictates he attend, Yassar Arafat, the chairman of the Palestine Liberation Organization, was making a valiant attempt to follow the droning speeches.

With his checkered keffiyeh raised off his ears for better hearing, the PLO leader, his face drawn, was fighting a losing battle against sleep. Finally, he gave up and dozed off until an aide gently nudged him awake.

Jarred into life by applause at the end, he smiled wanly, shook hands all around and, surrounded by his bodyguards, left for his Beirut office.

The image left behind was of a man under stress -- tense, preoccupied and sorely in need of a good night's sleep.

Arafat has good reason to be dejected these days. At a time when the Palestinians he claims to represent are in almost open revolt against their Israeli occupiers in the West Bank, Arafat and his fractious guerrilla movement are in disarray. They are immobilized by Arab feuds, polarized in the war between Iraq and Iran and sytmied by their own internal bickering and intrigues.

Probably not since 1970, when King Hussein of Jordan crushed the PLO's attempt to take over his kingdom, have things looked so dismal for Arafat and the PLO. While Arafat may be the wiliest politician in the Arab world and may once again ride out his troubles, the difficulties he faces now have pointed out, as never before, the extreme vulnerability of his movement.

Dependent on fellow Arabs' governments for virtually everything -- physical protection, diplomatic backing, arms, money -- Arafat has had to watch helplessly as the Persian Gulf war split his benefactors into antagonistic blocs with the PLO caught uncomfortably in the middle.

More damaging was the way the PLO's much advertised independence crumbled under the arm-twisting pressures of the two camps. When the showdown came before last month's divided Arab summit meeting, Arafat and the PLO were forced by Syrian President Hafez Assad, leader of the pro-Iran axis, to join a boycott of a summit whose aim was to organize a long-term strategy for the Palestinians' crusade against Israel.

Internationally, Arafat's hopes that this would be a year of great new diplomatic gains have been frustrated. A string of U.S. resolutions condemning Israeli policies in the West Bank and annexation of East Jerusalem have achieved little as have his efforts to involve Europe in the Middle East. His attempts to keep world attention on the Palestine issue have foundered against more immediate crises in Afghanistan, the Persian Gulf and Poland.

The PLO's military failures have been even more glaring. Despite professing support for PLO guerrillas, Syria's 30,000 groops in Lebanon have kept Arafat's fighters on a very short leash. It allows them to operate freely only in an exposed sliver of southern Lebanon where they are boxed in by Syrians to the north and a thin U.N. peace-keeping force to the south that tries to buffer them from artillery attacks by the Israeli-armed forces of renegade Lebanese Maj. Saad Haddad.

Despite 50 tanks and other heavy weaponry and boasts of being trained for such modern battle contingencies as chemical and even nuclear warfare, the PLO's forces remain motley and disorganized. Divided among the half dozen rival factions under the PLO banner, they not only have failed to present Israel with a real military threat but lately have not even been able to mount the sort of commando raids inside Israel that, in the past, bolstered their self-esteem.

Israel's war of attrition in southern Lebanon, has strained the PLO's manpower and morale to such an extent that it has begun drafting Palestinians from universities abroad.

The PLO's problems extend from the battered ranks of guerrillas in southern Lebanon to its leadership in Beirut and Damascus. As head of Fatah, the largest and most important faction in the PLO, Arafat's leadership of the guerrilla movement is not in doubt. But more military rivals are again plotting to reduce his influence on the 15-member executive committee and to force him to adopt policies such as the summit boycott that he clearly opposes.

Arafat, middle-class and conservative, is deeply suspicious of the way Arab governments have sought to manipulate the Palestinian issue to their own ends. He is a veteran of dozens of challenges from smaller, radical organizations such as the Popular Front for the Liberation of Palestine and has developed a genius for surviving by playing one off against the other.

Each crisis he has survived in the 12 years he has headed the PLO, however, has taken its toll and, as has finally become evident in the wake of the Persian Gulf war, reduced Arafat's freedom of action.

"He is the rubber man of Arab politics, bouncing back from each crisis," says one Western analyst, "but even a rubber ball loses some of its bounce each time it hits the floor."

Arafat has always depended on the natural elasticity of the Arab allegiances that have accommodated him either out of self-interest, as in the case of Syria, or out of fear of the trouble his followers could cause as in the case of Saudi Arabia and equally conservative Persiam Gulf sheikdoms.

The war between Iraq and Iran, both allies of the PLO, has reduced this elasticity by dividing the Arab world more than at any time since the 1960s.

Iraq's Saddam Hussen, one of the Arab world's most implacable socialist radicals, has welded a surprising new alliance with King Hussein of Jordan and King Khalid of Saudi Arabia, rulers he once plotted to overthrow. Around this core has emerged a bloc of the rich and vulnerable oil nations of the gulf and the other Arab moderates.

Against this powerful new alliance, Syria's Assad, a bitter personal rival of Saddam Hussein, has rallied his partners in the hard-line "steadfastness front," -- including Libya, South Yemen, and Algeria -- behind Iran in its war against Iraq.

Caught between these forces, Arafat tried desperately to remain neutral. He offered himself and the PLO as mediators in the war, largely aides said, to avoid taking sides. This accomplished nothing.

Then three weeks ago, as Arab leaders prepared for their annual summit meeting, Assad decided the time had come to show that, although a minority, he and his bloc could not be ignored. He demanded the summit be canceled and when that failed, he called for a boycott.

Arafat, forced to choose between Assad, on whom his PLO forces in Syra and Lebanon depend for survival, or Saddam Hussein and his oil sheiks who bankroll the PLO, tried desperately to temporize. On a shuttle through Arabia and Iraq, he unsuccessfully proposed a postponement of the summit and then pleaded for understanding on why he would probably be forced to follow Syria.

Assad seized on an apparently causal comment by President-elect Ronald Reagan about hopes of opening a dialogue with King Hussein, using it as an excuse to squeeze Arafat. Overnight Reagan's comment became a secret "Jordanian option" in the Syrian media, which saw King Hussein hoping to resume his role as spokesman for the West Bank Palestinians.

At the summit, Hussein reaffirmed, as did the final communique, that the only "legitimate" representative of the Palestinians remained the PLO.

But when Arafat had convened his executive committee in Damascus on the eve of the summit, the alleged "option" had gained a life of its own. Pushed by committee members beholden to Assad, the allegation provided the excuse for Arafat and his moderate supporters, against their judgment, to join the Syrian boycott of the summitt.

The big losers in the episode were Arafat and the PLO. Not only was their professed independence shown to be a sham, but by not attending the summit they forfeited their hopes of getting increased subsidies and a unified Arab policy on Israel with which to confront the Reagan administration.

PLO officials insist that their fellow Arabs understand their predicament and are sympathetic. A more realistic private assessment by PLO members, however, is that things are so bad in the Arab world that the summit had become meaningless.

"What we have is a deep split in the Arab world and we have been caught between it," said one U.S.-educated Palestinian professor with close ties to the PLO.

Arafat's aides admit privately the Syrians have the PLO "by the scruff of the neck" and there is not much he can do so long as they control his arms and supply lines in Lebanon.

"We are part of the Arab world and when the situation there is bad as it is today, we share it," said Mejed Abu Sharar, head of the PLO information department. "But the PLO has always succeeded in overcoming these dangers without losing our earlier political and diplomatic accomplishments. We will this time, too."