Maintenance support service network (MSSN) is used to provide maintenance services and maintain the operational status of equipment. However, the performance of MSSN has been significantly influenced by inevitable disturbance, which makes it vital to maintain its robustness. Existing research on robustness of MSSN mainly focuses on single-layer rather than two-layer network, which imposes constraints on the disturbances and limits its application. To solve these issues, this study develops a two-layer MSSN, consisting of a directed entity-layer and an undirected cyber-layer focusing on supporting maintenance service. A definition of robustness for two-layer MSSN is proposed, and effect propagation models are established to evaluate its robustness of MSSN, followed by its improvement strategies. In particular, two strategies applied in the single-layer MSSN are modified to adapt to the two-layer MSSN, and a novel greedy partnership building approach is proposed to find an optimal strategy under cascading failure, to maintain the robustness of MSSN from a complex network perspective. Finally, numerical examples are presented to illustrate the effectiveness of the proposed approach.