As agentic AI in education shifts from reactive tools toward partners that take initiative and persist over time, a central question is how learners relate to, evaluate, and benefit from artificial agency. We conducted a longitudinal experiment in an undergraduate learning analytics course, in which 17 student teams (N = 48) collaborated with a persistent LLM-based teammate across weekly sessions. The agent decided when to intervene through a trigger-based architecture, and its social role was manipulated between teams: a Cognitive Agent that challenged quick consensus or a Supportive Agent that invited quieter members to contribute. Combining chat discourse, post-session surveys, and spoken reflections, we identified distinct patterns unfolding across three timescales. Students accommodated their language to the agent's role immediately, using more social language toward the Supportive Agent from the first session. Their helpfulness evaluations were recalibrated from session to session in relation to the agent's observed behavior, rather than remaining anchored to students' pre-existing attitudes toward AI. A slower crossover emerged in perceived collaboration process and positive-affect word use in reflections: Supportive-Agent teams began below Cognitive-Agent teams and ended above them, although students rated the Supportive Agent less helpful throughout. Because these responses follow different trajectories, single-session evaluations of agentic AI may miss changes that emerge only through repeated interaction.

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