If he IS losing the dressing room, the answer is, and always will be, to change the dressing room. Even if that means offloading the entire squad of 25. And the reserves.
You never, ever, ever, ever, allow footballers to dictate who their manager should be or how their manager should manage. Ever. Under any circumstances.
if a few players have given up, and it looks like they might have, you get rid of them. Whomever they are. No questions. Gone.
You ALWAYS back the manager if you want to be a successful club. Especially a manager that has won as much as this one.