[CentOS] Not Responding To TCP Connections

I have a CentOS 3 box that appears to be having problems where a TCP
SYN comes into port 80 for an Apache Tomcat web application, but the
rest of the TCP "3-way handshake" isn't happening.  When the error
occurs, I always see this pattern in tcpdump:

  * A TCP SYN comes in from the client
  * ~3.25 second later I get another TCP SYN from the client
  * ~6.5 seconds after that I get a third and final SYN before the
client gives up
  * No TCP ACKs are returned to the client to continue the 3-way handshake

The box is accepting lots of connections on lots of different ports
and everything else seems to be working, but I'm occassionally getting
these errors on port 80 for the last few weeks (the box has been up
for a while).

Has anyone else run into anything similar to this?

Am I correct in saying that the Linux kernel, not java and/or Tomcat,
handles the TCP stack, including the 3-way handshake?  If so, getting
past the 3-way handshake should have nothing to do with Java or
Tomcat... IOW, this issue must have something to do with the OS,
right?

Suggestions welcome on this strange issue!

Thanks!