[squid-users] another Proxy-Connection Keep-Alive question

I've tried to play by the rules and check the mailing list archives
for an issue I am experiencing, but I believe my situation to be
slightly different than the Proxy-Connection issues previously
addressed.

I can understand how squid is unable to provide Keep-Alive persistent
connections in circumstances where the Content=Length of the origin
server's replies is no provided. However, I am seeing squid close
connections (with or without "Proxy-Connection: Keep-Alive"
specified) during Digest authentication header exchanges.

I've sniffed my browser dealing with squid, and the negotiation is
indeed transpiring over two consecutive sockets. First, the client
asks for the document, squid replies with a 407 providing the digest
auth parameters (nonce, realm, etc), closes my connection, then the
browser opens ANOTHER socket, providing the authentication response
which squid then approves, replying with an HTTP 200.

Is there a way to perform this exchange over a single socket? The
digest auth documentation I've found (including RFC 2617) seems to
imply that these requests can be performed over the same TCP connection.

Any help/pointers would be greatly appreciated,
Joe Boyle