`socat` does not always kill the child process

Question

I have a socat that spawns an ssh command:

socat "tcp-listen:${local_port},reuseaddr,fork,bind=127.0.0.1,keepalive,keepidle=10,keepintvl=10,keepcnt=2" "system:ssh -t -e none -o UserKnownHostsFile=/dev/null -o StrictHostKeyChecking=no -o LogLevel=ERROR ${user}@${host} <some command>

Sometimes it will happen that killing the socat process does not kill the ssh process. Is there a flag that I'm missing?