This error occurs when the game is not able to contact with the servers BattlEye service or with the BattlEye servers.
Check in Task Manager if this process is running and kill it with right click:
Go in these folders and check for BattlEye folders and delete them:
After that, please restart your Computer so running processes are closed. When done, please verfiy the game cache via Steam:
After that, start Arma 3 and check out under BattlEye if the setting is correctly set: