I was just thinking about what it would take to see Pep Guardiola getting fired!

I have always thought that it is impossible for him to ever lose his job and I still think it is, but from a hypothetical point of view, I wonder when a club's management would decide to sack him?

Four losses is of course not enough. He could probably lose 8 consecutive games and still wouldn't get fired. Probably 12... But it is a new situation that Pep Guardiola hasn't been in yet. This could either snowball and Manchester City is far more nervous than usually or they will soon answer with an impressive winning streak.
Management does not need to fire Pep Guardiola because his contract will expire at the end of the season, if they start to be dissatisfied with his performance due to the negative results achieved by Manchester City, then there will be no negotiation of a contract extension at the end of the season. Although Guardiola position is currently safe, he also has the responsibility to resolve the problems that occurred in the last four matches. Manchester City is threatened with not being able to continue its dominance if it does not immediately improve its quality and it will be an unpleasant farewell if the club and Guardiola decide not to continue their collaboration.
I don't think that City management will think of doing such a thing to see Pep as the major cause of their four consecutive losses, because it's first in history to happen with Pep in City. City players about 5 of them are injured which Rodri is part of them. We know the major role Rodri do play in the club, De Bruyne is not strong yet. A lot of injury truama here and there is enough for City management to understand that the club will not be in a good form. Real Madrid are also passing through theirs.