Basically, if mission is 'failed' she ignores those assigned to that mission and forgets their names. (Like that one time, she forgot Kon's name. I assume she has also forgotten Kaede and Akagi)
However, if it's 'betrayal', she'll have Nobimaru kill those who have betrayed her. (Kon not only has failed mission, but also betrayed Inari by choosing Kabane over her. Kaede and Akagi have simply lost to Kabane/failed their mission, so for now, they have been demoted/fired from special unit).
Robara's situation is considered as 'betrayal', because he no longer wants to fight for Inari and has abandoned the mission.
Nobimaru even warned Hinata ((and Robara)), that, in case of a betrayal, they'll have to run away and hide, going as far as adapting a new identity (new name/face). He favoured her, lol.