Italy's Amintore Fanfani tries to sort out his nation's political problems

Forty-two governments have come and gone in Italy since World War II. Because of the numerous political parties, shaky patchwork coalitions - alliances of necessity - are the best the political system seems able to produce. Skeptics call the situation ''permanent crisis.''

The failure last week of the first non-Christian Democrat-led coalition, at a time when Italy faces its most severe postwar economic problems, makes this government crisis much more serious than most.

The demise shelved Giovanni Spadolini's austerity package, which had already been partially approved by Parliament. The program was an attempt to whittle away $28 billion from the national budget through a complicated series of spending cuts and tax increases and to pare down inflation from 17 percent to 13 percent.

The collapse of the Spadolini coalition also prompted a breakdown in the 11 -month labor negotiations between union leaders and industry over automatic pay increases. A spokesman for Confidustria, the federation of industries, says the talks probably will not begin again until after a new government is formed. In the meantime, union leaders, who charged industry with profiting from the situation, called a general four-hour strike for Nov. 25. ''It is a potentially explosive social powder keg,'' said one Christian Democrat insider.

Following the failure of the Spadolini experiment, Italy has once again reverted to it's standby formula: a five-party coalition headed by the Christian Democrats, which, as the largest party, controls 38 percent of the vote.

At the request of President Sandro Pertini, Amintore Fanfani, a veteran Christian Democrat politician who has gone through the exercise four times previously in his long career, is hard at work trying to create Italy's 43rd postwar government. To do so, Fanfani needs the cooperation of four other parties - the Liberals, the Republicans, the Social Democrats, and the Socialists.

Only the Socialists, whose bickering with the Christian Democrats brought down Spadolini, are resisting. Led by Bettino Craxi, the Socialists are anxious to break the Christian Democrats' traditional hold on the premiership. They are driving a hard bargain: formal promise that Fanfani wil call new elections in May - one year early.

Political observers here say Fanfani has a good chance of succeeding in the negotiations.

The basis for this optimism lies as much in Fanfani's personal stature as in the drawbacks of the Socialists' push for early elections. ''One cannot underestimate the immense tactical resourcefulness of Fanfani,'' said one veteran of Italian poltics. ''He is able, sometimes with as little as a few sentences, to surmount what often seems an insurmountable problem.''

Fanfani is considered, along with Giulio Andreotti, among the most prestigious politicians in the Christian Democratic Party. Since 1976, Fanfani has been president of the Senate, the second most important post in the Republic following the President. In addition, he was instrumental in helping the Christian Democrat chief, Ciriaco de Mita, win his party's top post at the party congress last May.

The Christian Democrats feel Fanfani is the only candidate they will offer, says a party spokesman. Should the Socialists repudiate their most prestigious politician, it would be a humiliating blow. On the other hand, the Socialists desperately want new elections. They hope to boost their share of the vote from 10 percent (1979) to as much as 18 percent, although 15 percent is considered a more realistic figure. Yet they do not want to appear directly responsible for a protracted government crisis. Voters usually punish such maneuverings at the polls.

Traditionally, winter is a bad time to hold elections in Italy, so Mr. Craxi is attempting to negotiate his support for the Fanfani coalition through the spring if Fanfani promises to dissolve Parliament early. ''Not only is it dangerous, it is also useless. No government can be born programmed in advance how many months and days it will live,'' said a Christian Democrat spokesman scornfully.