The first time I watched this movie was 1982. Israel invaded Lebanon to stop the rockets that were then harassing northern Israel. The invasion was called “Operation Peace for Galilee,” and the Israeli army rolled all the way to Beirut. With their massive firepower, the Israelis assumed the Palestinians would cut and run, as Arab armies had in previous wars. But the Palestinians stood their ground.

It turned out the Israelis didn’t have a good endgame strategy in that war, any more than in the current one. In 1982, they accepted U.S. mediation that eventually forced the Palestine Liberation Organization to leave south Lebanon and Beirut. But this proved a mixed blessing, to put it charitably: The PLO guerrillas were replaced by more disciplined fighters from Hezbollah, the Lebanese Shiite militia created by the war.

Now it’s Hezbollah that poses the deadly rocket threat to northern Israel. Hezbollah suicide bombings forced Israel to invade Lebanon again in 1996 (“Operation Grapes of Wrath”), then to withdraw in frustration from Lebanon in 2000, then to attack Hezbollah once more in 2006 (“Operation Change of Direction”).

Gaza has been a similar exercise in frustration, with each cycle of violence buying a few years of quiet, followed by more war. The Israelis withdrew from Gazain 2005, only to have Hamas fire about 12,000 rockets and mortars at the Jewish state. The Israel Defense Forces invaded in 2008 (“Operation Cast Lead”), and a cease-fire followed. But in the years since, Hamas and other militias in Gaza have fired more than 3,000 rockets and mortars, despite periodic cease-fires.

On Nov. 14, the Israelis got fed up and retaliated (“Operation Pillar of Defense”) They assassinated Hamas military leader Ahmed Jabari, triggering 1,500 new Hamas rocket attacks, to which Israel responded by bombing more than 1,400 targets. The lopsided death toll (at last count, 130 Palestinians and four Israelis killed) led to some international criticism, which undercut some of the military benefits for Israel.

Is there any escape from this Israeli-Palestinian version of hell? The mark of an Israeli realist is to say, glumly, that this is as good as it gets. Few Israelis imagine that real peace is possible with adversaries who refuse even to accept Israel’s existence. The idealists who embraced the Oslo agreement of 1993 have died, moved away from Israel or given up.

Maybe it’s because of Thanksgiving Day, our national festival of optimism, but the idea that America should simply accept the inevitability of perpetual conflict on Israel’s borders seems like a betrayal of both sides. This kind of war grinds down the character of decent people, so Palestinians can cheer when they hear about rockets targeting the families in Tel Aviv, or Israel supporters can denounce newspapers for running a photograph of a sobbing Palestinian journalist cradling his lost child, or send e-mails headed, “Cue the Dead Baby.”

Acting as peacemaker in this conflict has been a thankless job for the United States. It begets enmity in Israel, which doesn’t want its closest ally to be “evenhanded” in this life-or-death conflict. And it begets cynicism and bitterness among Arabs, who have heard so many American promises, to so little effect, that many have concluded the process is a charade.

But at the beginning of Barack Obama’s final term, he needs to take up this burden once more, as he did when he came into office. He has worked hard to develop relationships with three important backers of Hamas — Egypt, Turkey and Qatar. Even the Israelis think that Egypt’s Muslim Brotherhood government has acted constructively in the crisis, and they’d like to see Egypt have more control of Gaza.

A cease-fire in Gaza would provide a new platform for negotiation — weird, unstable, but worth the effort of trying a few more steps. What’s the risk? Another war? The threat of future missile attacks? That dismal picture is called the status quo.a