Closing proxy to service socket when client is lost

We are using nginx, right now 1.6 to reverse proxy our services to the client. We are also using Server-Sent Events, a layer on top of HTTP that keeps the socket open.

Here is a piece of required config.

proxy_buffering off;
proxy_http_version 1.1;

Here is our setup

Client <---> nginx <---> Service
     Socket 1     Socket 2

When I close my browser without doing a proper disconnect, Socket 1 is closed while Socket 2 is still open. The Service is seeing that nginx is still connected and still is continuing to push messages on there.

Here is the scenario I'm seeing with wireshark.

Client -XXX- nginx <---> Service
     Socket 1     Socket 2

Is there a way to have nginx close Socket 2?

Would HTTP's Connection: keep-alive cause any adverse behavior?