It is not Manchester City that is going through that challenge, Manchester United have also been on the same boat foe a while with their fate still uncertain as they have a brand new manager. I recur that Bayern Munic also faced similar situation last season and there have been times we were thinking that Chelsea would be relegated due to misfortune that befell them in the league. So these are normal things that teams go through and came out stronger. The case of Manchester City is not really as bad as it is being portrayed because they still have a chance at winning the league.
Manchester City and United are both facing problems, it's just that the burden and pressure are completely different. Pep Guardiola may still be with Man City if they fail to win a trophy, but what makes his head spin is the responsibility he bears, and maybe his pride would be hurt if he didn't get a single trophy. While Man United may not be setting lofty targets, but what makes it tough is that no manager has been able to meet those expectations to date, and the burden that Amorim carried grew heavier because Nistelrooy left a good impression before he left.