We examined the influence of a parent on robot-assisted activities for a child with Autism Spectrum Disorder. We observed the interactions between a robot and the child wearing a wearable device during free play sessions. The child participated in four sessions with the parent and interacted willingly with the robot, therapist, and parent. The parent intervened when the child did not interact with the robot, considered “disengagement with the robot”. The number and method of intervention were decided solely by the parent. This study adopted video recording for behavioral observations and specifically observed the situations before the disengagement with the robot, the child’s behaviors during disengagement, and the parent’s intervention. The results showed that mostly the child abruptly discontinued the interactions with the robot without being stimulated by the surrounding environment. The second most common reason was being distracted by various devices in the play sessions, such as the wearable device, a video camera, and a laptop. Once he was disengaged with the robot, he primarily exhibited inappropriate and repetitive behaviors accentuating the symptoms of autism spectrum disorder. The child could re-initiate the interaction with the robot with an 85% chance through the parent’s intervention. This suggests that engagement with a robot may differ depending on the parent’s participation. Moreover, we must consider types of parental feedback to re-initiate engagement with a robot to benefit from the therapy adequately. In addition, environmental distractions must be considered, especially when using multiple devices for therapy.