I searching for a possibility to have mirrored pods of a nginx loadbalancer deployment in kubernetes that alle share the same kubernetes service with one single external IP. I tried the scenario with this statefulset config:

apiVersion: apps/v1
kind: StatefulSet
metadata:
  name: loadbalancer
  labels:
    run: loadbalancer
spec:
  serviceName: "loadbalancer"
  selector:
    matchLabels:
      run: loadbalancer
  replicas: 4
  updateStrategy: 
    type: RollingUpdate
  template:
    metadata:
      labels:
        run: loadbalancer
    spec:
      containers:
      - name: loadbalancer
        image: /services/infrastructure/loadbalancer:latest
        ports:
        - containerPort: 80
          protocol: TCP
        - containerPort: 443
          protocol: TCP
        volumeMounts:
        - name: certs
          mountPath: /etc/letsencrypt
  volumeClaimTemplates:
  - metadata:
      name: certs
    spec:
      accessModes: [ "ReadWriteOnce" ]
      resources:
        requests:
          storage: 100M

And this service config:

apiVersion: v1
kind: Service
metadata:
  creationTimestamp: null
  labels:
    run: loadbalancer
  name: loadbalancer
  selfLink: /api/v1/namespaces/test/services/loadbalancer
spec:
  clusterIP: 10.31.249.3
  externalTrafficPolicy: Cluster
  ports:
  - name: http
    port: 80
    protocol: TCP
    targetPort: 80
  - name: https
    port: 443
    protocol: TCP
    targetPort: 443
  selector:
    run: loadbalancer
  sessionAffinity: None
  type: LoadBalancer

All 4 pods are able to successful request the required let's encrypt SSL certs in parallel.

The problem is that the connection via the single service from outside the cluster via the external IPv4 address resets randomly.

How can this be prevented?