I do not believe checking the proxy logs will provide the answers of why the nodes are randomly getting disconnected. I would start in the central node, and check the logs/repo/trace/ I would check both "system_repo" and "audit_repo" ( I would check the times it failed) , then I would go to that node and check the same location. I would also check both Central's and RIm's Windows event logs (system and application). I hope this can provide to you more answers.
Giuseppe Novello Principal Technical Support Engineer @ Qlik