First WNB Corp.'s disclosure last week that it had reached an agreement to sell an interest in Women's National Bank renews some nagging questions about the staying power of women's banks.

And while there are no ready answers to those questions, at least one thing is certain in the case of Women's National Bank. By striking a deal with Washington banker Leo M. Bernstein, as it did last week, the holding company for WNB indicated it is willing to yield control by women in return for badly needed capital and continuation of a special identity.

Why else would First WNB accept Bernstein's offer to purchase an interest in WNB after spurning an offer from National Bank of Washington?

Although Bernstein is chairman of Security National Bank, he proposes to buy into WNB as a private investor. Bernstein won't discuss his motives or plans for WNB prior to making a tender offer that, if initiated, would come only after a careful review of WNB's books.

Several District bankers say, however, that First WNB considers Bernstein's offer more attractive than NBW's because Bernstein is prepared to retain the Women's National name and identity even though he might buy controlling interest in the five-year-old bank.

That might not have been the case had NBW's offer to merge with WNB been accepted. NBW's offer called for a stock swap that would have given it control of Women's National, but First WNB's directors rejected that proposal last weekend after considerable debate.

NBW Chairman Luther Hodges would only confirm that his bank made an offer to acquire Women's National and that it was rejected.

Sources close to the discussions say some First WNB directors had serious misgivings about establishing an association with a large institutional investor such as NBW whose principal stockholder is the United Mine Workers of America.

An amalgamation of the two banks would have spelled the end of Women's National and its charter as the first federally approved financial institution founded and controlled primarily by women. Selling one of the few remaining women's banks in the country without assurances that the new owner would uphold the founding principles is said to be unacceptable to its founders.

But a merger would have been the closest thing to a perfect fit for NBW and Women's National, some bankers believe. In its Capitol Hill branch, Women's National offers NBW an attractive location.

But more than that, acquisition of Women's National would have given NBW an important psychological gain in proving unequivocally that it was back on solid footing. What's more, it is possible that Women's National might have been operated as a subsidiary of Washington Bancorporation instead of being merged into NBW, the holding company's principal subsidiary.

Operating as a subsidiary of James Madison Ltd., the holding company for Madison National Bank, might also have been a possibility for WNB. Although there had been discussions of a possible merger between Madison and Women's National, no formal offer was ever made by Madison.

The bank recently reported a net loss for 1982 as well as an increase in loan losses. What's more, the WNB concedes it will be difficult to turn a profit in 1983.

Finally, all of these problems have been compounded by the recent departure of WNB's chief executive officer, Emily Womack, who resigned after being injured in a tragic accident. With financial problems and a void in leadership, WNB finds itself trying to avert the fate of other women's banks that didn't quite make it.

Alleging discriminatory lending practices in the mid-'70s, women's groups throughout the country rushed to organize banks to serve what they perceived as special needs of women. A few survived after shaky beginnings. Others failed.

The movement soon ran out of steam in several cities, especially after the passage of laws banning sex discrimination in matters involving women's attempts to obtain credit.

Women's National and others of that genre can take credit for changes in that regard, no matter how subtle. But the issue confronting the few surviving women's banks today is, can they succeed as limited special-interest institutions?