In mandatory.yaml, you can add

data: keep-alive-requests: "1000000"

kind: ConfigMap
apiVersion: v1
metadata:
  name: nginx-configuration
  namespace: ingress-nginx
  labels:
    app.kubernetes.io/name: ingress-nginx
    app.kubernetes.io/part-of: ingress-nginx
data:
  proxy-connect-timeout: "10s"
  proxy-read-timeout: "10s"
  client-max-body-size: "2m"
  keep-alive-requests: "1000000"
  upstream-keepalive-requests: "1000000"

Yes, it is possible for Nginx Ingress Controller.

But you need to use a ConfigMap for this, not an annotation.

keep-alive

Sets the time during which a keep-alive client connection will stay open on the server side. The zero value disables keep-alive client connections.

References: http://nginx.org/en/docs/http/ngx_http_core_module.html#keepalive_timeout

Here is the example:

apiVersion: v1
data:
  keep-alive: 0
kind: ConfigMap
metadata:
  name: nginx-configuration
  namespace: ingress-nginx
  labels:
    app.kubernetes.io/name: ingress-nginx
    app.kubernetes.io/part-of: ingress-nginx

For more information, visit the following links: Nginx Ingress ConfigMaps and keep-alive