amazon-ecs-agent: Too many open files

Yesterday we upgraded our cluster from amzn-ami-2016.03.c-amazon-ecs-optimized to the latest, amzn-ami-2016.03.g-amazon-ecs-optimized. At some point overnight, two of the instances in our cluster (out of ~6 in ASG) began flooding logs of this nature (hundreds per second):

Aug 17 07:21:17 Seelog error: open /log/ecs-agent.log.2016-08-17-14: too many open files
Aug 17 07:21:17 2016-08-17T14:21:17Z [WARN] Error retrieving stats for container bcbd3d6d2a51f656ec2066e62296010f5432262e1a564678325a60f3e642a575: dial unix /var/run/docker.sock: socket: too many open files

The two instances terminated without human interaction (not sure if that’s a coincidence of auto-scaling). Near the end, these logs also appeared:

Aug 17 07:21:17 2016-08-17T14:21:17Z [CRITICAL] Error saving state before final shutdown module="TerminationHandler" err="Multiple error:
Aug 17 07:21:17   0: Timed out waiting for TaskEngine to settle
Aug 17 07:21:17   1: Timed out trying to save to disk"

We haven’t experienced this on previous AMIs.