State-of-the-art space optical networks are built on top of the FC-AE-1553 standard which can support realtime applications. A hybrid space network system architecture using FC-AE-1553 fiber-optics (named FC) link together with optical wireless communication link (OWC, also known as LiFi) has been proposed to increase space optical network's mobility while supporting even higher bandwidth and lower latency. The advantage of the hybrid space network (HSN) is its high data rate capacity boosted by the OWC link. Its problem, on the other hand, lies in that the OWC link might be blocked by the solar sail panels when the spacecraft is orbiting around the earth. To tackle the link blockage issue, we propose a robust hybrid network structure, named RHSN by integrating the OWC link with conventional radio frequency (RF) link in parallel. When obstacles blocked the OWC link, the RHSN network can autonomously offload part of the routing data onto RF link and the FC-AE-1553 link, and thus ensuring continuous and stable signal transmission. However, the integration of RF and OWC links are challenging, since the RF link access is shared among different users, while the OWC support a device-to-device direct link whose link throughput can be guaranteed. To test the robustness of the proposed RHSN while supporting the data traffics when blockage happen, we designed a new link failure aware resource allocation algorithm for RHSN to work efficiently in different scenarios (with and without OWC link blockage) supporting parallel OWC and RF links, and performed numerical simulations. Simulation results demonstrate that the OWC link's traffics can quickly switch to the RF link and the FC link when the OWC link is down, with certain total throughput drop. Specifically, when compared with HSN network where only OWC link exists, RHSN can offer a performance improvement in terms of 5Gbps network bandwidth increments with a single access point and 52% average latency decrements, when the OWC link blockage happened in the low earth orbit.