As far as I can tell, Firefox is the only browser that regards "connection:
close" as an indication that the connection should not be counted against
the connection limit, and this behavior does _not_ follow the HTTP
recommendation regarding connections. Section 8.1.4 states that:
However, there are web apps in existence (e.g., Gmail)
that set the "connection: close" header to inform the
user-agent that the HTTP transaction is going to take
a long time. (This is also informative for the
server.) This allows a user-agent to not count this
connection against the RFC 2616 recommended maximum of
2 persistent connections per host.
Clients that use persistent connections SHOULD limit the number of
simultaneous connections that they maintain to a given server.
(All browsers use persistent connections, so all browsers are subject to the
recommendation stated below)
A single-user client SHOULD NOT maintain more than 2 connections with
any server or proxy.
There is no mention of only maintaining two persistent connections, all
connections (persistent or otherwise) are supposed to be counted against the
connection limit. In addition, there is no reason why long-lived responses
(those that shouldn't be counted against the connection limit) should have
to have their TCP connection closed after the response is fully received.
Therefore, I don't see "Connection: close" as an appropriate means for
advising that connections should not be counted against connection limits.