Children are back at school, the High Holidays are approaching and even the MKs are only a month away from the end of their extended summer vacation. As of next Friday, it will officially be autumn, when leaves fall from the trees and speculation will continue to intensify on the question of how long it will be before Prime Minister Ehud Olmert's government falls. Just as it is inevitable that a tree that once blossomed will soon be barren, so too a government that looked sturdy as an oak at the start of its tenure just four months ago, now seems like a tree without roots, barely clinging to the ground. But Israel's political system does not follow the forces of nature. In one of many ironies, the worse off a government's image, the likelier it is to last; and the stronger it appears, the more likely it is to fall. This absurdity is a product of the system of coalition governments. At a time when their reputation is at a nadir, none of the parties that make up Olmert's coalition has an interest in seeking elections. The Likud, which leads the opposition, also needs more time to rehabilitate from the electoral blow it received six months ago. And the many rookie MKs need more time and coverage to make a name for themselves before they seek re-election. So, no matter how many hunger-striking soldiers sleep on the lawn opposite the Prime Minister's Office, it is unlikely that Olmert will quit or get toppled before the winter. Five factors will decide the government's longevity: Its ability to pass the 2007 state budget in the Knesset; the Labor leadership race; the state of Kadima; the findings of the Winograd Commission; and the investigations into Olmert's real estate transactions and political appointments. Each of these issues is a tinderbox that could ignite and bring down the government. A BBC interviewer asked recently whether it was more likely that the war in Lebanon or "Israel's many sex scandals" would spur the next Israeli election. When told that if anything would bring down the government, it would be a vote on the state budget, the interviewer replied, "Israel is more boring than I thought." The budget survived its first test Tuesday when it passed in the cabinet with the support of all Labor ministers except party chairman Amir Peretz. Now it has to pass three readings in the Knesset plenum by March 31 or the government falls automatically, setting up June elections. It also must make it through the Knesset Finance Committee, where Labor is represented by MKs who have given the coalition headaches. The fact that six Labor ministers defied Peretz by voting in favor of the budget bodes well for the government's longevity. The biggest threat to the coalition is Peretz deciding to topple the government over the budget ahead of a potential leadership race in Labor. But if Labor MKs will not listen to their leader, the budget could pass on time in December for the first time in years. Peretz's antics ahead of the vote angered the other Labor ministers, who accused him of using them in a cheap gimmick to persuade the public that he is socio-economically minded and they are not. One minister vowed that Peretz would never regain his leadership over them. That promise is significant because the minister who made it intends to run against him for the Labor leadership. The war in Lebanon lost Peretz his base of power in the party that came from Labor doves and Israeli Arabs, who are Labor's largest sector. Labor bylaws require a leadership primary within 14 months after the party loses a general election, meaning that the next race will be no later than May, unless the party constitution is changed. Before the war, there was an effort underway to delay the race, which was expected to succeed. But now Peretz's potential predators smell fresh meat and are eager to devour him as soon as possible. Olmert's associates assume that whoever replaces Peretz will want time to prove himself ahead of a general election, and will want to extend the government's tenure - especially if the new leader replaces Peretz as defense minister, and if a new diplomatic process gets underway. That perception was confirmed by spokesmen for the leading Labor candidates. Olmert's associates said that after the budget passed the cabinet, he would consider expanding his coalition. They said Olmert was considering several options, including adding parties, making a move that would encourage Labor to leave and maintaining the status quo. It appeared at press time that the latter was most likely, because no opposition party had shown interest in joining the government, and Olmert knows that reshuffling portfolios could cause unnecessary unrest in Kadima. The party's voter registration drive will kick off soon with a battle to bring in members - one that could determine who will lead Kadima in the next election. The investigations into the war and Olmert's alleged improprieties are less predictable, because they are in the hands of judges and generals, not politicians. Olmert's associates assume he has nothing to fear from any of the inquiries. But more governments have fallen over scandals that were investigated than by budgets that failed to pass. Olmert's opponents need to be hoping that one of the inquiries bears fruit. If that happens, Olmert may have to make like a tree and leave.