Despite a recent jump in Coach's share price on signs of stabilization, Goldman Sachs issued a research note saying that the retailer's turnaround may be just midway through.
Previous attempts to reinvigorate blue-chip consumer companies, including Nike and Gap, have been long, expensive and painful, the report noted. Analysts also reiterated a "sell" rating on Coach stock.
"The average peak-to-trough share price move relative to the S&P 500 for this group is -63 percent, and the duration two and a half years," it said. "While Coach has already taken some pain, this analysis suggests it may only be half way through the worst of it."
(Read More: Coach Beats Earnings, Hikes Dividend)
Years of underinvestment and too much emphasis on its outlet stores have undermined Coach's brand equity, leaving it open to newer entrants to the space, include Fifth and Pacific's Kate Spade brand, Michael Kors, and Tory Burch.
The company's falling market share in the core handbag market and poor search trends reflect its deteriorating brand equity.
An analysis of Google search trends shows that the company fares relatively poorly in searches by consumers in more trendsetting states, such as New York and California, and more prominently in late adopter states.
"In our view, this portends poorly for market share trends going forward, as late adopters migrate to hot brands that are resonating in trendsetting markets," the report said.
To offset the pressure its core handbag business is facing, Coach has turned to its footwear and apparel business as strategic growth areas.
Goldman warned, however, that these areas are lower margin, require more store labor and inventory space, and that the success rate by other brands attempting to cross into new categories has been "spotty."
"Also, these growth initiatives are unlikely to do anything to fix Coach's problems in its core handbag business, and in a worst case may do harm by distracting the organization and confusing the customer," the report said.
To fix this core handbag business, Coach needs to resort to drastic measures including shuttering as much as one third of its outlet stores (whose lower prices may be hurting its brand) and increasing its marketing and design spending.
Still, Goldman noted that it has yet to see "decisive initiatives to fix its core North American handbag business," the success of which analysts said is directly tied to the future of its business.
—By CNBC.com's Katie Little. Follow her on Twitter
Goldman Sachs prohibits its analysts, professionals reporting to analysts and members of their households from owning stock of any company in the analyst's coverage area.