Pinochet's grip on Chile is jarred by economic and political challenges

The road is getting mighty bumpy for Chilean President Augusto Pinochet Ugarte, whose 9 1/2-year hold on power is under fresh and insistent challenge. The bumps are both economic and political:

* Chile's worst recession since the 1930s has plunged its copper-based economy into a tailspin. Several banks have failed, and some that are still in business have quit lending. The foreign debt is about $17 billion, and Chile is pledged to pay $9.3 million this year on that and on private sector debt, which the government has assumed. The unemployment rate is pushing into the mid-20s.

* Opposition to the Pinochet government, long stilled by the repressive tactics of that government, has gathered new strength and even traditional Pinochet supporters are openly questioning his programs and actions.

Some Chile watchers are reading a shift in the powers of one military officer in particular - Maj. Gen. Santiago Sinclair Oyender, head of the President's general staff - as a sign that Pinochet may be losing some of his grip. General Sinclair's powers have been extended to command of the President's advisory committee and he now is allowed to sign documents in Pinochet's behalf.

Through all this, General Pinochet has been keeping a low profile. But this month he again shuffled his Cabinet - the 12th shuffle of his rule - in what observers saw as a desperate effort somehow to shore up the economy. Last week Pinochet promised that, despite personnel changes, there would be no change in economic or political policies.

General Pinochet also went out of his way recently to talk of the ''monolithic unity'' of Chile's armed forces - a sign to some that there are divisions within the military and that General Pinochet may not be as sure of his power as he once was.

But Pinochet proved his staying power in difficult situations before and certainly plans to stay president. Still, growing economic gloom, which has cast a shadow over the whole country, is beginning to cost him some support.

No longer can he claim the economy is a success, as he had in the years just after the 1973 coup he led against the government of democratically elected President Salvador Allende Gossens. In the mid-'70s, inflation dropped from a rate of 600 percent a year to about 10 percent. A surge in exports helped to expand growth. Although some Chileans disputed all along that the economy had made major gains, it is hard to deny that exports brought prosperity to many parts of the economy at that time.

Many Chileans agreed with Pinochet's plans to move Chile from Allende's state-oriented economy to more of a free-enterprise system. Pinochet promises that the economic shift will continue. But the effort has been derailed, at least in part, as the government has stepped in to bail out many local banks and to embark on a variety of programs aimed at helping hard-pressed businessmen.

Growing criticism of Pinochet's economic policy is being heard despite new muzzles on the press. Some are calling on the government to find ways of aiding the millions of poor who are said to be suffering more than anyone in the current recession.

Such calls are not new. But what is new is that they are winning support from businessmen and bankers. The recent Christmas and New Year's period was a disaster for many in the Chilean business world. Sales were off 40 to 50 percent from a year earlier. Most business activity in Chile is at a standstill.

The problem seems to stem from government and business practices of over-extension in the past decade - rushing to buy goods from abroad, racking up huge foreign debts.

The Central Bank says government-incurred foreign debt is about $17 billion. Private debt, which has now been taken over by the government in an effort to help the private sector, runs to $4.3 billion. Much of the latter must be paid in 1983 and the government has to pay another $2 billion of its own debt by May, a full $5 billion by the end of 1983.

The weekly business magazine Estratejia noted that industrial output slipped 13 percent, maybe even 15 percent in 1982, the worst such record in all of Latin America. ''Now it is not just specific programs and policies which are threatened,'' it wrote, ''but the free enterprise system itself.''