Internet of Things (IoT) technologies are increasingly implemented in buildings as the cost-effective smart sensing infrastructure of building automation systems (BASs). They are also dispersed computing resources for novel distributed optimal control approaches. However, wireless communication networks are critical to fulfill these tasks with the performance influenced by inherent uncertainties in networks, e.g., unpredictable occurrence of link failures. Centralized and hierarchical distributed approaches are vulnerable against link failure, while the robustness of fully distributed approaches depends on the algorithms adopted. This study therefore proposes a fully distributed robust optimal control approach for air-conditioning systems considering uncertainties of communication link in IoT-enabled BASs. The distributed algorithm is adopted that agents know their out-neighbors only. Agents directly coordinate with the connected neighbors for global optimization. Tests are conducted to test and validate the proposed approach by comparing with existing approaches, i.e., the centralized, the hierarchical distributed and the fully distributed approaches. Results show that different approaches are vulnerable against to uncertainties of communication link to different extents. The proposed approach always guarantees the optimal control performance under normal conditions and conditions with link failures, verifying its high robustness. It also has low computation complexity and high optimization efficiency, thus applicable on IoT-enabled BASs.