Coach may be particularly vulnerable. The company, which spent 15 years as a sluggish subsidiary of Sara Lee until it was spun off in 2000, is largely credited with creating the "accessible luxury" category of retail and currently has sales of about $3 billion a year. Since its initial public offering, it has increased its share in the highly fragmented U.S. market for handbags and leather accessories from a tiny sliver to a dominating 22 percent of total sales. (The next closest brand, LVMH's Louis Vuitton, has about half that.) Because of such rapid growth, Coach has come to epitomize many of the operational assumptions about retail that have emerged in the past decade: that the concept of luxury is elastic, that labels can succeed without a diva designer, that brands must control distribution at all costs and stick to narrow markets where they can dominate.

But some analysts and investors worry that the very strategies that made Coach's ascent so spectacular may compound its challenges in a declining market. The consensus is that elite brands like Vuitton, Hermès, and Gucci are less susceptible to a recession because their customers will still splurge, regardless of the economy's ebb and flow. European brands are more diversified, producing ready-to-wear clothing that can offset a decline in handbags and accessories. Coach, meanwhile, sells mostly handbags and accessories (and it doesn't do business in Europe, where it would be unlikely to gain traction on a continent that is home to so many high-end fashion houses, so even the strong euro won't help).

But it would be foolish to expect Coach—or Frankfort—to go gently into that good night. The brand has spent the past eight years becoming an increasing threat to its centuries-old competition, and its C.E.O. intends to push even deeper into the market, despite the uncooperative economic climate. This intention may go down in the books as a study in hubris, but it may also wind up as a primer on how to run a growth company in a bear market. Considering Coach's short but spectacular life as a publicly held company, it could be argued that if Frankfort can't navigate the current environment, few C.E.O.'s can.

"When everything is going your way, you can tell yourself you're a genius," he says over a cocktail in early January. "But you're a fool if you believe it. I have every confidence that we'll continue to be as relevant and strong as ever, that our strategy will win out. But the truth is that for many years the wind was at our back. Now it's in our face."

C.E.O.'s aren’t known for acknowledging vulnerability, but one of Frankfort's favorite topics of conversation is his nightmares. A tall, trim man who signs his emails "Peace" and wears closely cut three-piece suits with open-collar shirts, he offers extravagant details of the recurring visions of failure that jolt him awake several nights a week. He even brings the dreams up during meetings with his sales staff (he sees the discussions as motivational). In one nightmare that he's had for years, Frankfort wanders the northern New Jersey house where he and his wife raised their children, confused and frightened by opposing views from two windows: bucolic countryside in one, and the Bronx housing project where he grew up appearing in the other. In a second dream, which he initially had during a New Year's vacation with his family in St. Bart's, he is walking down Madison Avenue on his way to an important meeting when he realizes that he has nothing on his feet but fuzzy blue socks. He bangs on the glass door of Cole Haan—a rising competitor in the handbag arena—begging for shoes, but no one is there. Panic mounts; the feeling of his feet against the pavement is unbearable. He wakes in a sweat. "My shrink says that I'm afraid I'm not prepared," he says. "I guess it isn't hard to figure out why."