Keep alive timeout not being respected on Amazon ELB

I'm using Tomcat 6.0.24 on Ubuntu (JDK 1.6) with an app that does Comet-style requests on an HTTPS connector (directly against Tomcat, not using APR).

I'd like to set the keep-alive to 5 minutes so I don't have to refresh my long-polling connections. Here is my config:

<Connector port="8443" protocol="HTTP/1.1" SSLEnabled="true"
           maxThreads="1000"  keepAliveTimeout="330000"
        scheme="https" secure="true"
           clientAuth="false" sslProtocol="TLS" />

Unfortunately it seems that the server closes the connection after 65 seconds. The pcap from a sample session goes something like this:

T=0   Client sends SYN to server, handshake etc.
T=65  Server sends FIN to client
T=307 Client sends FIN to server

(I'm guessing the 5 minute timeout on the client is due to the HTTP lib not detecting the socket close on the server end, but in any case — the server shouldn't be closing the connection that early)

(edit: this works as expected when using the standard HTTP connector)