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.
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."
Berkowitz added that he presented his firm's view in front of the Sears board in January, including his concerns about its cash burn. When he left, he said he "did not sense any disagreement among the board with any of the points that I raised."
The day he made his comments, Sears shares closed at $17.52. They were trading near $17 Thursday morning.
During the fourth quarter, Sears reported a loss of $580 million, substantially wider than its $159 million loss in the prior-year period. After the release, Neil Saunders, CEO of Conlumino retail research firm, told investors "there is worryingly little evidence to suggest a material improvement in either the performance of Sears or Kmart."
In a separate note to shareholders following the report, Sears' Lampert wrote:
"Because of Sears and Kmart's longstanding history and cultural impact, we are targeted for criticism when our results are poor. But it is unfair to evaluate our approach through the rearview mirror without acknowledging the changing circumstances in our industry as well as our bold attempts to change the way we do business to meet this changing reality."
Earlier this month, the company announced its intention to obtain a new senior secured term loan facility of up to $750 million. Moody's said the loan would improve Sears' liquidity but maintained its "negative" outlook on the department store.