Socially Assistive Robots are studied in different Child-Robot Interaction settings. However, logistical constraints limit accessibility, particularly affecting timely support for mental wellbeing. In this work, we have investigated whether online interactions with a robot can be used for the assessment of mental wellbeing in children. The children (N=40, 20 girls and 20 boys; 8-13 years) interacted with the Nao robot (30-45 mins) over three sessions, at least a week apart. Audio-visual recordings were collected throughout the sessions that concluded with the children answering user perception questionnaires pertaining to their anxiety towards the robot, and the robot's abilities. We divided the participants into three wellbeing clusters (low, med and high tertiles) using their responses to the Short Moods and Feelings Questionnaire (SMFQ) and further analysed how their wellbeing and their perceptions of the robot changed over the wellbeing tertiles, across sessions and across participants' gender. Our primary findings suggest that (I) online mediated-interactions with robots can be effective in assessing children's mental wellbeing over time, and (II) children's overall perception of the robot either improved or remained consistent across time. Supplementary exploratory analyses have also revealed that the gender of the children affected their wellbeing assessments with interactions effectively distinguishing between varying levels of wellbeing for both boys and girls for the first session and only for boys during the second session. The analyses have also revealed that girls have a higher opinion of the robot as a confidante as compared with boys. Findings from this work affirm the potential of using online mediated interactions with robots for the assessment of the mental wellbeing of children.