Existing multi-agent coordination techniques are often fragile and vulnerable to anomalies such as agent attrition and communication disturbances, which are quite common in the real-world deployment of systems like field robotics. To better prepare these systems for the real world, we present a graph neural network (GNN)-based multi-agent reinforcement learning (MARL) method for resilient distributed coordination of a multi-robot system. Our method, Multi-Agent Graph Embedding-based Coordination (MAGEC), is trained using multi-agent proximal policy optimization (PPO) and enables distributed coordination around global objectives under agent attrition, partial observability, and limited or disturbed communications. We use a multi-robot patrolling scenario to demonstrate our MAGEC method in a ROS 2-based simulator and then compare its performance with prior coordination approaches. Results demonstrate that MAGEC outperforms existing methods in several experiments involving agent attrition and communication disturbance, and provides competitive results in scenarios without such anomalies.