Predictability is important to autistic individuals, and robots have been suggested to meet this need as they can be programmed to be predictable, as well as elicit social interaction. The effectiveness of robot-assisted interventions designed for social skill learning presumably depends on the interplay between robot predictability, engagement in learning, and the individual differences between different autistic children. To better understand this interplay, we report on a study where 24 autistic children participated in a robot-assisted intervention. We manipulated the variance in the robot’s behaviour as a way to vary predictability, and measured the children’s behavioural engagement, visual attention, as well as their individual factors. We found that the children will continue engaging in the activity behaviourally, but may start to pay less visual attention over time to activity-relevant locations when the robot is less predictable. Instead, they increasingly start to look away from the activity. Ultimately, this could negatively influence learning, in particular for tasks with a visual component. Furthermore, severity of autistic features and expressive language ability had a significant impact on behavioural engagement. We consider our results as preliminary evidence that robot predictability is an important factor for keeping children in a state where learning can occur.