We explore how an AI model's decision fairness affects people's engagement with and perceived fairness of the model if they are subject to its decisions, but could repeatedly and strategically respond to these decisions. Two types of strategic responses are considered -- people could determine whether to continue interacting with the model, and whether to invest in themselves to improve their chance of future favorable decisions from the model. Via three human-subject experiments, we found that in decision subjects' strategic, repeated interactions with an AI model, the model's decision fairness does not change their willingness to interact with the model or to improve themselves, even when the model exhibits unfairness on salient protected attributes. However, decision subjects still perceive the AI model to be less fair when it systematically biases against their group, especially if the difficulty of improving one's qualification for the favorable decision is larger for the lowly-qualified people.