Connection header stripped on response

Okay, just as a sanity check I set up a simple PHP web server to send a few different headers through a simple BIG-IP reverse proxy VIP, with generic HTTP profile attached.

I see all of the headers coming through to the client, including Connection: Upgrade.

How are you verifying the missing Connection header? In a capture? And if so, where?

Try adding this simple iRule

when HTTP_RESPONSE_RELEASE {
    foreach x [HTTP::header names] {
        log local0. "header($x) = [HTTP::header $x]"
    }
}

and then tail the LTM log from the command line

tail -f /var/log/ltm