The scheduled electric vehicle (EV) charging flexibility has great potential in supporting the operation of power systems, yet achieving such benefits is challenged by the uncertain and user-dependent nature of EV charging behavior. Existing research primarily focuses on modeling the uncertain EV arrival and battery status yet rarely discusses the uncertainty in EV departure. In this paper, we investigate the EV charging scheduling strategy to support load flattening at the distribution level of the utility grid under uncertain EV departures. A holistic methodology is proposed to formulate the unexpected trip uncertainty and mitigate its negative impacts. To ensure computational efficiency when large EV fleets are involved, a distributed solution framework is developed based on the alternating direction method of multipliers (ADMM) algorithm. The numerical results reveal that unexpected trips can severely damage user convenience in terms of EV energy content. It is further confirmed that by applying the proposed methodology, the resultant critical and sub-critical user convenience losses due to scheduled charging are reduced significantly by 83.5% and 70.5%, respectively, whereas the load flattening performance is merely sacrificed by 17%.