Intelligent agents have become prevalent in everyday IT products and services. To improve an agent's knowledge of a user and the quality of personalized service experience, it is important for the agent to cooperate with the user (e.g., asking users to provide their information and feedback). However, few works inform how to support such user-agent co-performance from a human-centered perspective. To fill this gap, we devised Co-Performing Agent, a Wizard-of-Oz-based research probe of an agent that cooperates with a user to learn by helping users to have a partnership mindset. By incorporating the probe, we conducted a two-month exploratory study, aiming to understand how users experience co-performing with their agent over time. Based on the findings, this paper presents the factors that affected users' co-performing behaviors and discusses design implications for supporting constructive co-performance and building a resilient user-agent partnership over time.