SECRETARY OF STATE George Shultz's belated peregrination through the Middle East notwithstanding, the prognosis for the future of that volatile region is nothing but grim. The low-keyed secretary may finally win an agreement for the withdrawal of Israeli, Syrian and Palestinian troops from battered Lebanon, but not even the most sanguine optimists expect him to make real progress towards the broader regional peace to which President Reagan has committed his prestige.

The now-likely failure of the Reagan policy is as lamentable as it is dangerous. The tragic history of the violent conflict between Israelis and Arabs over the last 35 years has proven that the absence of peace invariably means a continuation of war.

True believers in the "Israeli Might Makes Right" school have argued that the Middle East conflict could be quickly resolved if only Israel was left to its own devices. But this argument hinges on a superscillious fallacy -- that Arab determination to avenge perceived wrongs is no match for the Israelis' determination to impose their dominion on their fellow Semites.

In a region famous for centuries- long blood feuds between families, tribes or sects, the notion that 4 million Israelis can impose their will indefinitely on more than 200 million Arabs smacks of naive, wishful thinking. Such talks sounds like the dangerous and insecure prattle of the neighborhood bully; it neglects the historic fact that lasting peace among diverse peoples does not come from the barrel of a gun, but from the mutually agreed tolerance of relative equals.

Given the Middle East protagonists' ever-mushrooming firepower, the only certain prediction we can make today is that the next explosion will be more deadly and destructive than any previous one. And one of these days the explosion could be nuclear. That prospect should give statesmen around the globe cause for alarm. But if the future continues to mirror the experiences of the past, we will only appreciate the potential for another devastating outburst of violence when it is too late to prevent it.

The White House will dispute such pessimism, of course. It still refuses to acknowledge the flop of its peace plan, which was as flawed in its conception as it was mismanaged in its execution.

The president's dogged optimism, dutifully reiterated by Shultz before and during his shuttle diplomacy, is so little reinforced by fact that it looks suspiciously like a smokescreen to blur the true dimensions of the debacle of the administration's Middle East policy. Excessive protestations of the president's continued commitment to seeking a genuine regional peace only raise new doubts. Increasingly it appears that not only has Reagan's policy has failed in the Middle East, but also his will.

With next year's presidential elections already beginning to distract Washington, domestic politics are once again encroaching on national policy. This will prove especially true for policy toward the Middle East. Because the Reagan initiative has produced more frustration than success, and because a significant bloc of American voters devoted to Israel shares Menachem Begin's negative attitude toward the Reagan plan, it is only a matter of time before the truculent and unrewarding Middle East question gets shelved for the duration of the campaign.

Already President Reagan's political handlers have become alarmed by private White House polls showing that his Middle East policy has alienated a great many of the nation's Jewish voters. To reverse this politically dangerous trend, the president is being pressed to cut his losses in the Middle East and switch his attention to more manageable issues more likely to sway an unpredictable electorate.

These political pressures are reinforced by an increasingly popular analysis of the Middle East which argues that the time has come for a period of U.S. diplomatic passivity. According to this view, the rebuff of the latest American efforts to spur negotiations relieves the Reagan administration of any further responsibility, and that the U.S. no longer needs feel it has a central role in resolving the Mideast's problems.

It now seems likely that President Reagan will heed this advice and abandon his active Mideast diplomacy, at least for the duration of the presidential campaign. Secretary Shultz hinted as much in a recent remark to reporters: "It may be that the best thing we can do now is to keep quiet for awhile."

In fact, Shultz's high profile mission to the Middle East seems to confirm the shift in administration policy. For despite all the upbeat claims that his role is to breathe new life into the Reagan peace initiative, Shultz's primary task is damage control. His mission is to salvage Washington's tarnished credibility in the area by finding a face-saving accord on Lebanon. But despite the attention it has recently received, Lebanon remains but a tragic sideshow to the wider, more intractable, Arab-Israeli conflict.

But if the president succumbs to the temptations to deemphasize his Mideast diplomacy, that decision will be shortsighted and perrilous in the long run. The recent history of diplomacy in the Middle East does show that active U.S. involvement in the search for peace is frustrating and dangerous. But the same history proves that exercises in non-involvement -- what the diplomats like to call "back-burner" diplomacy -- invariably lead to new disasters, each more damaging to U.S. interests -- and threatening to world stability -- than the last.

To turn one's back on the unpleasant realities of the Middle East, as some now counsel, is not an escape from failure and frustration, but rather a guarantee of unavoidable future involvement in much graver trouble to come. No good can come from a passive reliance on the region's suicidal dynamics to put things right.

It is an exercise in the politics of the absurd to talk of American disengagement from the Middle East. Disengagement is impossible because of our strategic interests in the region's ultimate stability, our government's commitments to important allies such as Israel, Egypt and Saudi Arabia, and the perceived need to check any Soviet advances into a region whose oil is so vital to the capitalist world.

Washington may not be able or willing to determine the course of events in the Middle East as it might wish. But to suddenly abandon all efforts to influence political developments in the area would not only be an act of folly, but could lead to unspeakable new horrors that could engulf nations far beyond the Middle East.

The terrible progression of the five nasty wars between Israel and the Arabs since 1948 demonstrates the huge stakes the United States and the entire world have in Middle East stability. The first Arab-Israeli war in 1948 was fought with horse cavalries, small arms, and homemade armored cars built onto truck chassis. By the fifth and most recent war in Lebanon last summer, the combattants had raised the ante of violence to include day-long duels of heavy field artillery, the introduction of such ghastly instruments of destruction as phosphorus shells and cluster bombs, the blitzkrieg of fleets of modern tanks, and the relentless dive bombings of such sophisticated state-of-the-art jet planes as Israel's U.S.-made F16s.

The next war, if it is not avoided, can only prove worse. But the most frightening -- and, alas, not unimaginable -- prospect is a nuclear war at some future date if peace continues to elude the region. A nuclear exchange would be a logical conclusion to the frightening arms race produced by the Middle East conflict over the years.

Though Israel has studiously avoided admitting the fact, Western intelligence organizations generally agree that Israel has had atomic bombs since at least 1973. Today, it is believed, Israel has the components for seven to 10 such weapons -- enough to drop one on each major Arab capital -- stored in underground shelters. They could probably be armed for delivery in a matter of minutes.

Israel obviously understands that its monopoly of nuclear weaponry in the Middle East is not unchallengeable -- hence the reckless decision to bomb two French-built nuclear reactors that were being installed outside of the Iraqi capital of Baghdad in 1981. Israel justified the bombing on the grounds that those reactors could be used to manufacture an Arab nuclear bomb.

But it would be foolish to bet that Israel will forever be able to prevent the Arabs from acquiring their own bomb. Given the financial resources of the Arabs, the all-too-easily mastered technology involved, and the thousands of Arab students studying nuclear physics in universities around the world, an Arab nuclear bomb cannot be more than a decade away.

If the world cannot somehow impose a viable peace in the region before then, the Middle East could well become the Sarajevo of World War III. It is to avoid that horrendous prospect that Washington must continue to search for a peace, no matter what frustrations result or what humiliations come from failures of policy. Domestic political considerations aside, the Reagan administration, and its successors, must wake up to the perilous consequences if the Middle East conflict is not resolved before a nuclear holocaust makes the whole question academic.