The only time I have seen the club stick with the coach during this kind of form is Arsenal with Arteta two years ago.
They didn't have a win for over 2 months, players were trying to mail it in on their 3rd coach in a row, but the club said fuck that, get in line, he is staying.
Seems to have worked out for them, but a serious talk needs to be had with the players by the management. Otherwise they will continue to mail it in and the sack is just being delayed for nothing.