Using a social robot has been proven to have multiple benefits for the training of children with Autism Spectrum Disorder (ASD). However, there is no clarity on the impact of the interaction quality between a child with ASD and a robot on the effectiveness of the therapy. Previous research showed that the use of a robot in Pivotal Response Treatment (PRT) could be an effective treatment component in diminishing ASD-related symptoms. Further analyzing the data from a randomized controlled trial of PRT treatment, we looked at the long-term effects of child–robot game interactions to see whether the interaction quality changes over time. The attention and the engagement of six children were measured through the observation of non-verbal behavior at three different stages in the treatment that took 20 sessions per child. The gaze and arm/hand behavior of the participants towards the robot, the game, and other present humans were observed. The analysis showed no significant decrease in the attention and the engagement of the children towards the robot and the game. However, the attention and engagement toward the parents of the children increased. We conclude that the main result of sustained attention and engagement with the robot is due to the personalization of the games to meet the specific needs of this user group. These specific needs are met through inclusion of variability to the level of development and personal choice of each participating child. We see the additional finding of increased attention towards the parents as especially positive since the children are expected to improve in human–human interaction as a result of this treatment.