Following a goalless draw at Carrow Road, Manuel Pellegrini's side has now failed to win in consecutive league matches since October - a run of 21 games.
Such faltering form not only leaves them nine points behind league leaders Leicester City, but within two points of West Ham in fifth and in danger of not having Champions League football to offer when Pep Guardiola arrives next season.
Despite the fact the Canaries have the second-leakiest defence in the league, Sergio Aguero and co could not capitalise on last week's thrashing of Aston Villa and registered three shots on target against Norwich.
As demonstrated in the graph below, it means only Aston Villa have gone longer without recording back-to-back wins than City.
City are the only club in the top four to have gone longer than 10 games without back-to-back wins, although Chelsea's stuttering start under Jose Mourinho saw them go 23 games without recording six points from six.
In contrast, Arsenal and Tottenham have only had four and five games respectively in between consecutive victories.