Allen Weiner, senior technologies analyst at Gartner, said that Yahoo! board members, including activist investor Carl Icahn, are growing increasingly "unhappy" with Yang.
Weiner said: "It is pretty clear that the decision not to accept Microsoft's offer was not a good move. Yang is in trouble."
Yang led Yahoo!'s rejection of Microsoft's $44.6bn (£27.4bn) takeover bid in May. Since then, the internet giant's share price has continued to fall and closed yesterday at $12.39, more than $20 below Microsoft's bid price of $33 per share.
However, Yahoo! shareholders voted in favour of Yang and his fellow directors remaining on the board at the company's annual meeting in August of this year.
Billionaire investor Icahn, who has built his stake in Yahoo! to 5%, had been pushing for the complete removal of Yahoo!'s board.
However, Yahoo! ended the shareholder tussle by offering Icahn a seat on the board for him and two of his proposed directors -- former Viacom and Universal Studios chief Frank Biondi and former Nextel Partners boss John Chapple.
The news of continued unrest comes as Yahoo! looks to cut its global staff numbers by as many as 1,500 people.
Earlier this week the company revealed that profits had fallen by two-thirds in the last quarter and it was laying off 10% of its workforce in a bid to cut costs and boost productivity.
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