Based on the information provided in the support ticket, adding the annotations service.beta.kubernetes.io/azure-load-balancer-ipv4: 'xxxx' and service.beta.kubernetes.io/azure-load-balancer-health-probe-request-path: '/healthz' should help in maintaining a static IP address for your Kubernetes Ingress Controller.

Backup existing YAML

kubectl get deployment ingress-nginx-controller -n ingress-nginx -o yaml

Change existing YAML

Get new ingres version with sha

https://github.com/kubernetes/ingress-nginx/releases

  labels:
    app.kubernetes.io/component: controller
    app.kubernetes.io/instance: ingress-nginx
    app.kubernetes.io/name: ingress-nginx
    app.kubernetes.io/part-of: ingress-nginx
    app.kubernetes.io/version: 1.12.2 -> Change

  template:
    metadata:
      creationTimestamp: null
      labels:
        app.kubernetes.io/component: controller
        app.kubernetes.io/instance: ingress-nginx
        app.kubernetes.io/name: ingress-nginx
        app.kubernetes.io/part-of: ingress-nginx
        app.kubernetes.io/version: 1.12.2  -> Change

  image: registry.k8s.io/ingress-nginx/controller:v1.12.2@sha256:03497ee984628e95eca9b2279e3f3a3c1685dd48635479e627d219f00c8eefa9  -> Change

kubectl apply -f nginx-deployment.yaml

Check Upgrade

kubectl get pods -n ingress-nginx
kubectl describe deployment ingress-nginx-controller -n ingress-nginx