In children–robot interactions, an impression of a robot’s “social presence” (i.e., an interactive agent that feels like a person) links positively to an improved relationship with the robot. However, building relationships takes many exposures, and there is an intellectual gap in how social presence and familiarity collaborate in modulating children–robot relationships. We investigated whether social presence altered over time, how repeated exposure and social presence affected rapport, and how social presence would modulate children’s attitudes toward the robot. Fourteen children (four female, age = 10.79 ± 1.12) interacted with a companion robot for four days in spontaneous interactions. The findings revealed that children who perceived the robot as having a higher social presence developed a stronger rapport than those who perceived a lower social presence. However, repeated encounters did not change the children’s perceptions of the robot’s social presence. Children rated higher rapport after repeated interactions regardless of social presence levels. This suggests that while a higher social presence initially elevated the positive relationship between children and the robot, it was the repeated interactions that continued solidifying the rapport. Additionally, children who perceived a higher social presence from the robot felt less relational uneasiness about their relationship with robots. These findings highlight the importance of robots’ social presence and familiarity in promoting positive relationships in children–robot interaction.