Sears' second-largest shareholder has sold off more than 700,000 of the department store's shares this month, after a string of recent moves to boost its stake in the struggling retailer. According to SEC filings, Bruce Berkowitz's Fairholme Capital has sold 706,600 Sears shares since the beginning of March, reducing its ownership to 27.3 million shares. That's down from the more than 28 million shares it owned in February. Still, Fairholme remains Sears' second-biggest shareholder, owning roughly 25 percent of its outstanding shares. CEO Eddie Lampert has the biggest holding, at 29 percent.

Customers leave a Sears store in Chicago. Getty Images

A representative for Fairholme did not immediately respond to CNBC's request for comment. Sears has said that it does not comment on shareholders. Sears stock has fallen 16 percent so far this year, and is down 53 percent over the past 12 months. But Berkowitz, who was named to Sears' board last month, told Fairholme investors in February that his thesis on Sears "cannot be disproven." "Sears has a vast real estate empire complemented by unique businesses. Sears also has constraints, and we understand those constraints," Berkowitz told Fairholme investors on a February conference call. "The facts tell us that we own valuable assets at historic discounts. The facts determine our confidence and willingness to stay the course. Either Sears' price is going to climb to our assessment of intrinsic value, or we are wrong about that value and it will decline toward the current stock price."