U.S. envoy Philip C. Habib flew to Saudi Arabia today in an apparent effort to breathe life back into his flagging peace mission, which was imperiled anew today by the downing of a pilotless Israeli reconnaissance aircraft over Syria.

The drone, shot down by Syrian aircraft, was the seventh claimed by Syria and the fourth acknowledged by Israel since Syria moved surface-to-air missiles into eastern Lebanon April 29 in reply to the destruction of two Syrian helicopters by Israeli warplanes.

The downing, the first accomplished by aircraft rather than missiles, took place somewhere northeast of Damascus, according to a Syrian military spokesman who later announced that military exercises had been carried out at an unspecified location.

Although drone losses have become relatively common occurrences, today's raised fears here that Israel may be planning to destroy the missiles in the Bekaa Valley or mount a major attack against Palestinian guerrilla targets in southern Lebanon.

Such speculation has been reinforced by tough recent statements by Syrian President Hafez Assad warning that "Israel will not find it easy to destroy the missiles" and renewed warnings by Israeli Prime Minister Menachem Begin that Israel will destroy them if they are not removed.

Habib's second trip to Saudi Arabia, during which he was expected to see Prince Fahd, the day-to-day chief executive, was thought to focus on two interconnected problems.

First, Habib hoped to discover what went wrong at key meetings last Sunday and Monday, when Saudi Arabia and Kuwait failed to nail down a permanent cease-fire and framework for a political settlement in this divided country.

That plan, widely viewed as U.S.-backed, was further endangered by Israel's raid against Iraq's nuclear reactor.

After that raid, conservative Arab states headed by Saudi Arabia were believed less willing to take an active role in aiding U.S. diplomatic efforts because of U.S. support for the Jewish state.

Since the inconclusive meeting here the general security situation in Beirut and its suburbs has improved, although it remains far from what was considered normal before the current crisis began April 2.

However, the eastern, mainly Greek Catholic city of Zahle, which has been under siege ever since, continues to be shelled by its Syrian and Lebanese leftist besiegers.

According to many observers here, the various rival parties have until June 23 -- when another Arab League meeting on Lebanon is scheduled in Saudi Arabia -- to solve their differences. Thereafter, failing such an accord, there is general fear of a return to violence.

So far, the right-wing Christian militias have refused to cut ties with Israel -- as Syria has demanded -- and the Syrians and their Lebanese allies have refused to give the Lebanese Army greater responsibilities as the militias want.