Dorcas Hardin, the sophisticated Georgetown boutique that has catered to the well-to-do for more than 20 years, will shut its doors on March 1, according to the owner.

The store was acquired only two years ago by Val Cook, whose major credentials as a retailer at that time were her status as one of the store's best customers, and her own personal style.

The victim of a poor selling season that has produced unprecedented markdowns in small and large stores across the country, Dorcas Hardin also has had its share of typical Georgetown shopowners' problems. The decline in customers, who have shifted to other centers with easier parking, and shoplifting by what Georgetown merchants regard as "professionals" who work the Wisconsin Avenue strip, have taken their toll on profits and business in the stores.

"It's too hard for a small store to compete with the big ones like Saks and Bloomingdale's," said Dorcas Hardin, the store's founder, who added that she will miss having her name on the store. Cook "owns" the name for 10 years, Hardin said, by the terms of the sale two years ago.

"I feel awfully badly about it. It was my life's work," she said. "But I do understand that beautiful and well made clothes are very expensive and it is very had to get people to pay those high price tags."

High price tags were, in fact, not always a store problem, according to Cook. "If the clothes were interesting and unique, like Mary McFadden's designs, or handsome like the Bill Blass clothes, we sold them well." Last fall, during McFadden's two-day appearance at the store, Cook sold $32,000 worth of merchandise.

Women turned out to buy the $1,000 Bill Blass items, too. The shop racked up $22,000 in sales from his visit, and $12,000 in the two days that Joan Sibley and Dory Coffee had their samples of matte jersey dresses, at an average of $300 each at the store.

When selling wasn't a problem, persuading customers to pay their bills was, "I would say to myself. 'Gee, if I don't pay those Saks bills right away I'll get awful hassle and dunning letters from their lawyers,'" admits a deliquent billpayer. "But as for Val, I would reason. "She's an old pal, and she'd understand; I'll pay her later."

If Cook understood, the manufacturers with whom she did business in New York didn't. "Few manufacturers would extend credit to smaller stores, and I had to pay 'up front" (in advance) for all deliveries," she said.

And the merchandise she bought would frequently be delivered to the larger stores months before it reached Dorcas Hardin. "Even Loehmann's (the discount store) sometimes got a dress before I did."

When Cook bought store in January, 1975, it was a business that had established its success by selling expensive clothes to super-rich and social Georgetown women. Cook, whose only related experience at that time had been as a shopper for herself and her friends, felt that elegant clothes had had their day, and that the store needed to cater to younger customers with trendier items.

She started to order sportswear items and cheaper dresses until then had been untypical of the shop.

"I jumped at the suggestions of anyone and anything I thought would boost the business," Cook admitted. "My godmother suggested some patchwork dresses from the Napa Valley and I ordered them sight unseen. That may have been my worst bomb."

She made plenty of mistakes without anyone's help. "I barely sold a piece of the Calvin Klein separates in white wool flannel I bought a year ago," she said. "This year everyone is asking for white wool and I don't have it. Isn't that ironic.?"

Cook consoles herself that this fall she had clothes she considered perfect for her customers. "I looked around the shop one day and decided that they were the right clothes at the right prices. Tailored, wearable clothes that customers couldn't resist."

But customers resisted, at her shop and others around the country. Prices were high enough and styles uninteresting enough to inhibit women from buying.

(Cook has company in shutting down. Stanley Gans closed the doors of his exclusive women's specialty shop in the Spring Valley shopping center on Massachusetts Avenue in September. Margy and Betts, a more popularly priced clothing store in Alexandria, plans to close in February.)

Meanwhile, the shoplifters continued to bedevil Val Cook, she says. "We caught a woman with three Ultrasuede jackets under her coat," she recalled. "And we never saw the five Beged-Or suede coats leave the store, but they were shoplifted."

Cook never tried the electronic tags that most Georgetown shops use as an exercise in caution. It might well have offended her customers, she feels, and, according to other shopowners, the shoplifting "pros" have learned how to beat the system anyway.

There were customers, of course, but not enough. And some of them wore the clothes at least once and returned them a little soiled - "insisting of course, that they never wore them," Cook says angrily. "But how do you tell your friends who are customers that you know they aren't telling the trugh?"

Cook will tell her sales staff today that after a final sale, she will turn the key in the door of her shop and walk away on March 1.

"I loved being in retailing, and I loved the store. But it took too much time from my family for the reward I got from it," she said. "There just wasn't enough time to give proper attention to the store, the family and Seventh Avenue."

She'll probably stay in retailing, assisting private customers and maybe eventually linking up with another store. At the moment she is assisting Joan Mondale, wife of the Vice President-elect, with her wardrobe.

Before the store closes, she has a date to speak to the retailing classes at Mount Vernon College. "If they still want me, that is. And if they do, do I have a lot to tell them?"