The firm, which once drew teen shoppers with ads featuring scantily-clad models, has struggled more recently with falling sales.
But shares rose in May after the firm, which also owns the Hollister brand, said it was considering selling itself.
The stock plunged more than 21% on Monday after those talks ended.
Abercrombie boss Arthur Martinez said the firm's business plan offered a better bet for shareholders than a sale.
"We believe in the prospects for our business and the opportunities for our brands," he said in a statement.
"We are committed to taking sound, aggressive action to deliver enhanced performance and long-term stockholder value."
Abercrombie reported a quarterly loss in May, with sales down 4% year-on-year. The firm is one of many US retailers seeing uncertain growth this year.
But Mr Martinez said the firm had seen "solid" sales momentum at its Hollister stores and expected to see improvement in the second half of the year.
Abercrombie operates about 900 stores globally. The potential buyers had reportedly included American Eagle and Cerberus Capital Management, a private equity firm.
Investors dumped shares of Abercrombie & Fitch on Monday after the Ohio clothes retailer said it had broken off talks with potential buyers.