Very interesting question and I think Manchester City management will not sack Guardiola even if Manchester City crashes out of the EPL given the merits to the club.
But now I don't think Guardiola is to blame for City's defeats, but rather injuries to a huge number of City players and partly City's not very active transfer policy this season. Most of City's victories have come from players that Guardiola bought a few years ago.
Besides, Guardiola's contract is about to expire and maybe he himself wants to leave City for some Saudi clubs to make money.
Pep did many things for Manchester City, helped them to win many titles so it's possible that Manchester City will respect him and allow him to complete a season, even it is bad, before they separate with each other at the season ending or in the summer transfer season.
Pep Guardiola doesn't want to stay at a same club for too long and Manchester City is where he stays longest so far. Soon the party will end and he already won Champions League with them, so it's not too serious if he leaves. I believe that Manchester City will have bigger problem if Pep leaves the club, because Pep can find many big clubs in Europe to work with, if he want.
Guardiola has done what no coach in the history of Manchester city has done for club, he practically transformed Manchester city into an elite club, winning all the important trophies in club football, the champions league, the premiership, the FA cup, the FIFA world club championship, now if you were the owner of the club, will you sack a manager of such repute because he lost four games in a row?
There are many reasons for Manchester City to keep Pep Guardiola but the coach has many reasons to end his era in Manchester City. Pep Guardiola is a coach like Zidane, when he feels enough, he will leave. Manchester City will not be able to convince Pep Guardiola to stay especially if the coach himself feels that he already hits his limits and players there hit their limits too.