Facing uncertain and dynamic demands over different days, logistics companies need to adopt adaptive solutions for the last-mile delivery. Meanwhile, one of the major barriers for implementing vehicle routing problem (VRP) algorithms in real world dispatching systems is the stability of delivery driver's routes and schedules. To establish a theoretically sound and practically useful solution framework, this paper aims to optimize robust and consistent space-time paths for the multi-day VRP by providing daily schedules with limited variations from the master schedule. A multi-commodity network flow-based optimization model is proposed to minimize generalized transportation costs and the daily deviation of day-dependent space-time paths among demand analysis zones. Lagrange relaxation (LR) methods and alternating direction method of multipliers (ADMM) are used to handle complex side constraints. Experiments on illustrative networks and Beijing delivery network are developed to demonstrate the effectiveness of the proposed method.