Allardyce's contract expires in June.
Brown, who was Allardyce's No2 at Bolton Wanderers, told talkSPORT: "I think it will be a big mistake if they move on Sam.
"What more can he do? He put his credentials on the line [when he joined West Ham].
"He's been a Premier League manager for the last decade and he's gone down into the Championship to pull them up by their boot laces and take them into the Premier League. Now they are middle of the table.
"I know they are not safe but if you take it all into consideration, only the top six are safe, excluding Liverpool. For me, what more can he do?"