ssh-agent does not remember identities when running inside a docker container in DC/OS

I am trying to run a service using DC/OS and Docker. I created my Stack using the template for my region from here. I also created the following Dockerfile:

FROM ubuntu:16.04
RUN apt-get update && apt-get install -y expect openssh-client

WORKDIR "/root"
ENTRYPOINT eval "$(ssh-agent -s)" && \
           mkdir -p .ssh && \
           echo $PRIVATE_KEY > .ssh/id_rsa && \
           chmod 600 /root/.ssh/id_rsa && \
           expect -c "spawn ssh-add /root/.ssh/id_rsa; expect \"Enter passphrase for /root/.ssh/id_rsa:\" send \"\"; interact " && \
           while true; do ssh-add -l; sleep 2; done

I have a private repository that I would like to clone/pull from when the docker container starts. This is why I am trying to add the private key to the ssh-agent.

If I run this image as a docker container locally and supply the private key using the PRIVATE_KEY environment variable, everything works fine. I see that the identity is added.

The problem that I have is that when I try to run a service on DC/OS using the docker image, the ssh-agent does not seem to remember the identity that was added using the private key.

I have checked the error log from DC/OS. There are no errors.

Does anyone know why running the docker container on DC/OS is any different compared to running it locally?

EDIT: I have added details of the description of the DC/OS service in case it helps:

{
 "id": "/SOME-ID",
 "instances": 1,
  "cpus": 1,
  "mem": 128,
  "disk": 0,
  "gpus": 0,
  "constraints": [],
  "fetch": [],
  "storeUrls": [],
  "backoffSeconds": 1,
  "backoffFactor": 1.15,
  "maxLaunchDelaySeconds": 3600,
  "container": {
                "type": "DOCKER",
                "volumes": [],
                "docker": {
                "image": "IMAGE NAME FROM DOCKERHUB",
                "network": "BRIDGE",
                "portMappings": [{
                                  "containerPort": SOME PORT NUMBER,
                                  "hostPort": SOME PORT NUMBER,
                                  "servicePort": SERVICE PORT NUMBER,
                                  "protocol": "tcp",
                                  "name": “default”
                                 }],
                "privileged": false,
                "parameters": [],
                "forcePullImage": true
               }
  },
  "healthChecks": [],
  "readinessChecks": [],
  "dependencies": [],
  "upgradeStrategy": {
                      "minimumHealthCapacity": 1,
                      "maximumOverCapacity": 1
                     },
  "unreachableStrategy": {
                          "inactiveAfterSeconds": 300,
                          "expungeAfterSeconds": 600
                         },
  "killSelection": "YOUNGEST_FIRST",
  "requirePorts": true,
  "env": {
          "PRIVATE_KEY": "ID_RSA PRIVATE_KEY WITH \n LINE BREAKS",
         }
  }