Despite aggressive action on all sides, the Lebanon stalemate seems to be deepening. Although few are saying so publicly, Middle East analysts here are coming increasingly to the conclusion that the United States and Israel must come to terms with a continuing Syrian military presence in Lebanon.
Neither the Americans nor the Israelis appear likely to be willing to sustain the kind of casualties that it would take to drive the Syrians out of Lebanon. Public opinion in both the US and Israel leans heavily against deeper involvement by either country in Lebanon. In the US, the so-called Vietnam syndrome is still in evidence. In -Israel, there is widespread disillusionment with the nation's Lebanon involvement.
Regardless of the retaliatory US air strikes launched against his forces, Syria's President Hafez Assad holds many strong cards, in the view of analysts here.
''Assad understands the post-Vietnam syndrome and he expects the pressure to build on Reagan from the US Congress,'' said an Israeli defense analyst visiting here. ''He also feels that he can wait out Israel. The US and Israel are susceptible to political pressure which Assad doesn't have to deal with. He's playing brinkmanship with a deck stacked in his favor.''
At the same time, administration officials are working on the assumption that neither the Syrians nor their Soviet backers want to engage in a full-scale war in Lebanon. Syria is still engaged in the complicated process of absorbing sophisticated new military equipment supplied by the Soviet Union. The Soviets are involved in a prolonged leadership crisis and appear to be preoccupied with the issue of new American missiles in Europe.
Given the limits on US and Israeli involvement in Lebanon, the Reagan administration is depending heavily on the Lebanese government and Army to play a more assertive role in expanding their authority. But in private, administration officials admit that the US is leaning on a weak reed - the Amin Gemayel government.
US officials are convinced that if the Gemayel government does not grow stronger, increased American military pressure may fail to stabilize the situation. But some Lebanese contend that the US air strikes on Syrian positions may simply harden Syrian attitudes, making it more difficult for their government to reach any kind of negotiated accommodation with Syria.
In an appearance on the ABC television program ''Good Morning America'' on Monday, former Secretary of State Henry A. Kissinger argued that to try to expand the Lebanese government's control to the whole of Lebanon was an ''unobtainable'' objective. Mr. Kissinger asserted that a more obtainable objective for the US would be to let the Syrians dominate the northeast of Lebanon but not the whole country. The Israelis would have to continue to exert an influence in the south of the country. Christian Lebanese would hold the city of Beirut. In other words, the country would be partitioned, but in a way which would stabilize the situation.
In order to achieve such stability, however, Kissinger insisted that the US must ''show determination that we're not going to be driven out of Lebanon.''
Reagan administration officials are now attempting to do precisely that. They are trying to make it clear to Syria that the US cannot be driven out of Lebanon by military force or terrorist attacks. President Reagan himself has warned that US forces would strike Syrian positions once again, as they did on Sunday, if American forces come under attack. But Reagan also said that the US does not seek a wider conflict with Syria.
Joseph Sisco, a Middle East specialist and former Undersecretary of State, said that the combat between Syrian and American ground and air forces over the weekend underscores the importance of reconciling feuding Lebanese factions. He said that the Syrians had been ''unhelpful'' in furthering the conciliation process and had encouraged ''sectarian strife'' among the Lebanese.
''But I don't believe that the Syrians will be able to impose a political solution on the Lebanese any more than the Israelis were,'' said Dr. Sisco in an interview.
Sisco asserted that Syria may have miscalculated when it comes to Israel. The Syrians may believe that the Israelis will eventually have to leave Lebanon under any circumstances and that all Syria will have to do is wait. But Sisco said that without a negotiated agreement, the current situation, involving a major Israeli presence in south Lebanon, could persist for a considerable time.
The recently agreed-upon enhanced ''strategic cooperation'' between the US and Israel was aimed at moving matters to the conference table in Lebanon, Sisco said. He said that criticism of this cooperation from Arab nations friendly to the United States was to be expected but did not change the situation.
Syria is not going to compromise in Lebanon unless the US and Israel show a willingness to use ''both carrot and stick,'' said Sisco.
In Nuremburg, West Germany, on Monday, US Defense Secretary Caspar W. Weinberger said that the US is considering ways to improve the US Marine defenses in Beirut, including moving them to new positions.
The Defense Department, meanwhile, described as ''very successful'' its air strikes on Sunday against three Syrian positions. Officials said that 28 US Navy planes destroyed an SA-9 antiaircraft missile site, hit four other targets in another area, and seven targets in yet another. Two US planes were shot down.