Bill Witham, who performed as Napper Swan, is believed to have been assaulted on 6 September, police say.
The force said it believed Mr Witham was assaulted outside a property in Rochford at about 17:20 on 6 September. Bill Witham, 68, was taken to hospital in a life-threatening condition and died on 25 September. A man has been arrested after a musician died in hospital two weeks after being assaulted.