The mobile satellite communication networks (MSCN) enable network expansion and supplement in remote areas. Users in these regions can obtain specific network services with low latency and high transmission rates utilizing the low-earth-orbit (LEO) satellite constellation. However, due to the frequent switching of MSCN topology, the challenge is how to ensure the quality and continuity of data transmission paths in a certain time period. In this paper, we build a user satisfaction (US) indicator to measure the performance of pathfinding. The MSCN pathfinding optimization problem for the maximum US is first formulated. To simplify the complex calculation, we utilize the special-temporal division to solve the problem in two stages. In each time slot, the modified heuristic algorithm is utilized to find paths for the maximum US. Then, an active time slot division scheme is proposed. The divided time slot sequences are disconnected and reorganized to seek the time-extended optimal solution. Simulation results show that the proposed scheme achieves superior performance in improving the total US and guarantees reliable service continuity for MSCN.