We study an alternating-offers, bilateral bargaining game where players may derive disutility from accepting shares below what they deem as fair. Moreover, we assume that the values they attach to fairness (i.e., their sensitivity to violations of their fairness judgments) decrease over time, as the deadline approaches. Our results offer a new explanation to delays and disagreements in dynamic negotiations. We show that even mutually compatible fairness judgments do not guarantee an immediate agreement. We partially characterize conditions for delay and disagreement, and study the changes in the length of delay in response to changes in the model parameters.