For the second time in only 10 months, American International Group may lose in its bid for another insurance company.

In May 1997, AIG lost in its struggle to take over Golden Eagle, a workers compensation insurer in California. Liberty Mutual won that round after a confusing process that involved the state insurance commissioner, a judge, a host of lawyers and two, maybe three, other suitors for Golden Eagle. Some aspects of the acquisition are still being resolved in California courts.On Wednesday, AIG took a step that could allow Cendant to acquire American Bankers Insurance Co. of Miami. AIG, which had made an offer in December to take over American Bankers for $2.2 billion, said it would allow the two companies to discuss combining but they had only until 2:00 pm Monday to do so.

AIG's capitulation follows Cendant's move last Monday to raise its bid for American Bankers to $67 a share in cash and stock from $58 a share.

But if American Bankers and Cendant reach an agreement, AIG will receive a $100 million breakup fee from American Bankers and $10 million from Cendant.

In December 1997, AIG, a large New York-based insurer, proposed to acquire American Bankers, an insurer that writes insurance on unpaid credit card bills and loans, for $47 a share, or about $2.2 billion.

A month later, Cendant made an unsolicited offer of $58 a share, or about $2.7 billion. Cendant, a marketing and franchising concern that controls brands such as Ramada hotels and Avis rental cars, was formed late last year from the merger of HFS Inc. and CUC International. The company has headquarters in Parsippany, N.J., and Stamford, Conn.

AIG in early March matched Cendant's offer.

With the increase in Cendant's offer on Monday, the value of American Bankers has jumped nearly $1 billion in roughly three months.

The big winners are the American Bankers shareholders, who have seen the value of their holdings skyrocket in the last few months.