Multi-robot systems rely on underlying connectivity to ensure reliable communication and timely coordination. This paper studies the line-of-sight (LoS) connectivity maintenance problem in multi-robot navigation with unknown obstacles. Prior works typically assume known environment maps to formulate LoS constraints between robots, which hinders their practical deployment. To overcome this limitation, we propose an inherently distributed approach where each robot only constructs an egocentric visible region based on its real-time LiDAR scans, instead of endeavoring to build a global map online. The individual visible regions are shared through distributed communication to establish inter-robot LoS constraints, which are then incorporated into a multi-robot navigation framework to ensure LoS-connectivity. Moreover, we enhance the robustness of connectivity maintenance by proposing a more accurate LoS-distance metric, which further enables flexible topology optimization that eliminates redundant and effort-demanding connections. The proposed framework is evaluated through extensive multi-robot navigation and exploration tasks in both simulation and real-world experiments. Results show that it reliably maintains LoS-connectivity between robots in challenging environments cluttered with obstacles, even under large visible ranges and fragile minimal topologies, where existing methods consistently fail. Ablation studies also reveal that topology optimization boosts navigation efficiency by around $20\%$, demonstrating the framework's potential for efficient navigation under connectivity constraints.