With limited coaching resources, automated training devices offer opportunities for self-directed sports practice. However, their practical value depends on users’ continued use. To identify the key determinants of continuance intention toward basketball shooting training machines, this study integrates the Unified Theory of Acceptance and Use of Technology (UTAUT) and Task–Technology Fit (TTF) into an analytical framework. A mixed-method design was adopted, including prototype experience, interviews, and questionnaire surveys. A total of 429 valid questionnaires were collected from basketball enthusiasts recruited from universities, fitness centers, and public basketball courts. The results indicate that performance expectancy, task–technology fit, and effort expectancy all positively influence continuance intention. Among these factors, performance expectancy shows the strongest direct effect (β = 0.44, p < 0.001). In addition, task–technology fit reinforces both performance expectancy and effort expectancy. To translate these findings into design practice, the study further integrates the Function Analysis System Technique (FAST) and the Function–Behavior–Structure (FBS) framework, generating a design pathway from behavioral mechanisms to functional elements and structural implementation. These findings provide theoretical and practical support for the design of automated training devices.