Every Easter for the past few years, Chancellor Helmut Kohl has adhered scrupulously to an ascetic ritual: he holes up at an Austrian lakeside resort to shed some excess pounds and shore up his spirits for political challenges ahead.

This year, as he pursues his annual two-week retreat with the avowed aim of losing 15 pounds, the conservative West German leader appears to be facing a more troubling agenda than he could have anticipated only a few months ago -- and his difficulties do not concern merely a thick waistline.

With national elections 10 months away, members of the governing Christian Democratic Party are becoming increasingly worried about their prospects of clinging to power under Kohl's leadership.

For more than a decade, Kohl's political strength has derived from his dominance over the party apparatus and provincial voters. But now even once loyal supporters are expressing doubts about his future.

The announcement two weeks ago that the Bonn public prosecutor was opening a second investigation into the possibility that Kohl gave false testimony before a parliamentary inquiry into the country's biggest political corruption scandal has scrambled party plans for the next election.

Many Christian Democrats now concede that if either investigation should lead to an indictment, Kohl will be compelled to resign. His likely successor, Finance Minister Gerhard Stoltenberg, already enjoys a much higher approval rating in public opinion polls, and Christian Democratic officials openly profess that their party would have an easier time defeating the opposition Social Democrats with Stoltenberg at the helm.

The muffled response of the Social Democrats toward the launching of judicial proceedings against Kohl appears to confirm that view, for the opposition seems to recognize that a sitting chancellor weakened by scandal will represent its least formidable adversary in next year's election.

Johannes Rau, the opposition Social Democratic candidate for chancellor, also has seen his popularity slip in recent weeks. Rau is a more charismatic politician on the stump than Kohl, but his party has failed to generate much enthusiasm among voters because of confused economic and security policies.

Social Democratic officials believe that Rau could make a much better run against Kohl than a more popular opponent such as Stoltenberg.

Kohl's political woes have grown, ironically, as his government's record has improved. Falling oil prices and soaring exports have ensured a thriving economy, which normally would guarantee political success in West Germany. Kohl has established closer ties with his country's two most important allies, the United States and France, while maintaining satisfactory relations with East Germany despite tension between Moscow and Washington.

Still, Kohl's image has been sullied by successive scandals and frequent bickering within his center-right ruling coalition. One of the more divisive issues has centered in recent months on what kind of role West Germany should play in the Reagan administration's research into space-based missile defenses.

Bonn and Washington signed two accords Thursday that set forth terms for West German firms to participate in the "Star Wars" program and to engage in transfers of advanced technology.

Public dismay with the government's feuding, as well as anxiety about persistent high unemployment, has resulted in a series of setbacks in state elections for the Christian Democrats. A key barometer for Kohl's political destiny is expected to come with a state election in Lower Saxony this June.

If the Christian Democrats perform poorly, Kohl is likely to encounter growing pressure to step aside as his party's candidate for chancellor in the national vote next January.

Kohl's most serious personal challenge may now loom in the decisions to be handed down in coming months by prosecutors in Bonn and Coblenz on whether he should be indicted on perjury charges.

Both investigations result from claims filed by Otto Schily, a radical lawyer and leading member of the opposition Greens political party. Schily argues that Kohl lied to two parliamentary committees looking into political payoffs by the Flick industrial empire in return for favorable tax legislation.

The chancellor is accused of giving false testimony in November 1984 before a Bonn committee during which he allegedly covered up receipt of about $23,000 from Flick in the late 1970s that ostensibly never was recorded by the party's treasury. The money purportedly was pocketed by Kohl's longtime secretary, Julianne Weber.