People deeply care about how fairly they are treated by robots. The established paradigm for probing fairness in Human-Robot Interaction (HRI) involves measuring the perception of the fairness of a robot at the conclusion of an interaction. However, such an approach is limited as interactions vary over time, potentially causing changes in fairness perceptions as well. To validate this idea, we conducted a 2x2 user study with a mixed design (N=40) where we investigated two factors: the timing of unfair robot actions (early or late in an interaction) and the beneficiary of those actions (either another robot or the participant). Our results show that fairness judgments are not static. They can shift based on the timing of unfair robot actions. Further, we explored using perceptions of three key factors (reduced welfare, conduct, and moral transgression) proposed by a Fairness Theory from Organizational Justice to predict momentary perceptions of fairness in our study. Interestingly, we found that the reduced welfare and moral transgression factors were better predictors than all factors together. Our findings reinforce the idea that unfair robot behavior can shape perceptions of group dynamics and trust towards a robot and pave the path to future research directions on moment-to-moment fairness perceptions