Some of the reasons are:
None of the major parties have sufficient majority to be able to rule without courting the favors of the smaller parties. Israel is a bitterly divided country with many unsolved questions, among which are: the question of the settlement with the Arabs on the territories (which includes the extent of anti-terrorism measures, the talks with the opposing side leadership or the absence of such, matters which are acceptable or not acceptable to discuss there, the policy regarding Jewish settlements on the territories, the status of Jerusalem and especially Arab neighborhoods of Jerusalem, etc.), the questions of economic policy and welfare policy, the questions of the place of the religion (mainly meaning Judaism of course) in the state, the questions of labor laws and union privileges, and many more. For many of these questions, positions of the smaller parties are very hard to reconcile.
For the smaller parties, it makes a lot of sense to drive a hard bargain with many of these positions and extract concessions - monetary or lawmaking - from the major party to be part of its coalition and allow the major party to rule. On the other hand, for small parties with loyal electorate, it is very little reason to fear the elections - there's very high probability that they will keep their representation nearly unchanged. This makes it harder to preserve the coalition since for some parties, the talks become "my way or highway".
On the other hand, for a major party elections can be very convenient if they expect that the situation on the ground changed in a way that would allow them to have stronger position or more agreeable coalition partners and since as described above they always have "hard-bargaining" partners, they could pass the responsibility for the elections onto them. Since many of these small parties do have a loyal electorate, it is a win-win situation - those who vote for that small party keep doing it because they "didn't sell out", while those who didn't are energized by the desire to "show these bastards" and strengthen the other side. Since neither side is able to achieve domination, and the only way to try and gain tactical advantage is the elections, the elections happen more frequently.
Alternative to this may be so called "national unity government" where major parties come together to form a broad coalition. However those are usually unstable since the incentive for each one to break the coalition and have all the pie for itself instead of sharing it with others appears too great. Those usually dissolve as each party wants to try and take over. One of the most notorious examples of it is known in the Israeli politics as "the stinking trick". Reading it you can see all the machinery in motion - attempts at power grab, selling political power, fickle coalition partners, high price paid for their temporary loyalties, etc.