Vanquished in a circulation battle among Japan's three giant newspapers, the mass circulation Mainichi Shimbun ran up a distress signal on its front page recently and admitted virtual bankruptcy. After heavy losses - $29.5 million in 1976 alone - the daily has announced a lastditch plan to stem the tide of red ink.

Executives hope the 105-year-old Mainichi, Japan's oldest newspaper, can be saved. "We're a national institution so no one, not even the banks, wants to pull the trigger and put the grand old newspaper to death," said deputy editor Leo R. Amano. "But if we keep losing money we shall die. Time is very short now."

With a 4.5 million circulation, the Mainichi and its two competitors, the Yomiuri Shimbun (7.2 million) and the Asahi Shimbun (7.15 million) are mammoth operations. The Japanese are the most avid newspaper-readers in the world; 58 million papers are sold every day to a population of 111 million.

The big three newspapers campaign for subscribers with a magnificent disregard for cost. No American or European newspaper approaches the awesome size and scale of the forces deployed by Mainichi, the weakest of the three.

The paper employs 1,900 journalists, bases them in 360 offices all over Japan, and transports them in fleets for chauffeured, flag-flying limousines, three airplanes and five helicopter.

Private telephone lines allow swift transmission of facsimile pages to five printing plants. Every day the paper publishes 180 regional editions, - 24 pages in the morning and 10 in the evening - delivered to subscribers' homes by 80,000 distributors and delivery boys.

Unfortunately, Mainichi's debts and failures are on the same grand scale. The paper owes $258 million - much of it lost in wildcat gambles on unsuccessful diversification schemes - and the interest payments are crippling. In the last three years, Mainichi went another $65.5 million in the red.

he balance sheets are so appalling that an ordinary business would have gone into bankruptcy. Instead, the Sanwa and Mitsubishi banks, two of the paper's biggest creditors, have rallied round and supporting the rescue plan. The idea is to freeze interest payments and transfer publication of Mainichi in September to a new debt free company.

Mainichi reporter Kunio Naito calculated that even if profitability returned it would take 750 years to pay everyone off.

The 6,700-strong payroll may have to be reduced by 1,200 and the Mainichi labor union is opposed. The existing company is entirely owned by Mainichi staffers and they fear the influence of bankers in the refinanced paper will end the paper's journalistic independence. Deputy editor Amano believes the union resistance will fave because there is no real alternative.

Editorial freedom will be guaranteed, he said. The banks and other big business investors in the $17 million offspring company are certain to insist on tough management and an end to profligate spending.

In 1952 Mainichi was Japan's best-selling newspaper. Some of its staffers and many outsiders blame the slide on poor management by good journalists, who proved, when promoted to be soft-headed businessmen, "They had a succession of bad managaments - ineffective, irresponsible and spendthrift," said a veteran Tokyo journalist.

Amano attributes Mainichi's problems to "stupid . . . chaotic . . . and excessive competition in the newspaper industry." Asahi, which has a kind of Ivy League aura, is locked in bitter rivalry for sales supremacy with the popular, aggressive-managed and fast-rising Yomiuri Shimbun. The strugle intensified in December when Yomiuri for the first time edged Ashi out for the No. 1 spot for presitige and drawing power with advertisers.

"Both want to expand their circulation and the natural tendency is to gang up on us as the weaker one," Mainichi's Amona said.

The Japanese newspaper business abounds in quaint irrationalities. No one wants to be the first to raise prices, so the customer gets a month's worth of morning and evening newspapers delivered to his home for a bargain $6. The Asahi Shimbun makes a profit of about half of one per cent of revenues. The Yomiuri, which owns a baseball team and other profitable sidelines, does better. The Mainichi just piles up debts.

The sales drive used to be called "the pot-kettle war," because of the gifts salesmen used to woo subscribers. These days the gift include alarm clocks, pocket calculators and electric blankets.

Theoretically, the big three made an agreement to outlaw pressure sales tactics. They occur, it is explained, when "distributors go out of control." Each company has contracts with about 5,000 distributors, usually small shopkeepers. The middlemen keep secret the names of their customers, the newspaper readers, and are sometimes tempted to defect with their entire list to another newspaper.

The three papers sell in every remote village in Japan. They find immense armies of reporters, and refuse to use an available and much cheaper wire service.

Well-respected for its editorial quality, Mainichi was specially praised for its coverage of the Lockheed scandal last year. The cost was immense. As an example, the paper maintained a two-man, 24-hour watch on the home of key figure Yoshio Kodama. Relays of writers worked out of a limousine permanently stationed outside Kodama's house for three months.

In spirit, the newspaper, war, most closely resembles armed conflict and frequently borrows the same terminology. "In the circulation struggle, Mainichi was defeated on every battlefield," said an Asahi executive.

The first journalists of the Meiji restoration in 1868 came from Samurai families. The martial spirit survives among modern-day reporters who consider it a dishonour to be scooped.

Shunji Taoka, an Asahi reporter who welcomes the competition, declared: "It has nothing to do with economics. It is like warfare."