Richard Baker has been put on notice by shareholders after the Boots chief executive issued his second profits warning this year.
As well as the disappointing trading update, the chain announced last week it would sell off drugs business Boots Healthcare International (BHI), owner of Nurofen, Clearasil and Strepsils. The cash will then be returned to shareholders.
But some investors believe the U-turn - Mr Baker said in January that BHI was a core business - is just a sop to make up for the poor trading.
They are also becoming ever more frustrated with Mr Baker's performance.
"He's in last chance saloon territory," said one. "He's done a lot of simple stuff - he's cut a lot of jobs, for instance - and has done a lot of sale and leasebacks on the property. But now he's reached for the ultimate plan B and is selling off arguably the best part of the business."
Valuations of up to £1.25bn have been put on BHI, with giants such as Reckitt Benckiser and GlaxoSmithKline touted at possible buyers.
Mr Baker had a tough time ahead of him, the investor added. This view was echoed by a former Boots manager, who said that Mr Baker had six months to start showing an improvement at the retailer before losing the backing of the board. "The most important thing is the role of [chairman] Sir Nigel Rudd," he said. "He will have no qualms about pointing the revolver at Richard Baker: he's not going to give him the benefit of the doubt beyond a certain point. He would rather be remembered as the guy who fired Richard Baker than the guy who let things drift."
Last week's gloomy update from the chain prompted the credit agency Standard & Poor's to downgrade its credit rating, while equity analysts swiftly cut forecasts.
It also drew out interest from potential private equity buyers. A spokesman for Blackstone conceded the group was "probably" looking at Boots, while others thought to be interested included fellow US outfit Texas Pacific and UK players CVC Capital, Cinven and Permira. Buyout firm Kolhberg Kravis Roberts is also thought to be a contender. Boots, however, has a market value of nearly £5bn, meaning a consortium bid would be more viable.
All this puts even more pressure on Mr Baker, who took over the top job in 2003 after former incumbent Steve Russell quit.