There was nothing out of the ordinary in /var/log/messages. The logging just stops after the network card drops offline. dmesg also shows nothing out of the ordinary when the driver is loaded. The network card works fine until it is under heavy load.
Since you are running CentOS 3 I am assuming this server has been in production for some time. Did these symptoms just start? Did you do any updates before this started happening? Did you install this equipment, or did you assume admin duties from someone else? Maybe it had the HP net driver installed, and a kernel update broke that.
It appears to be a faulty NIC card. We moved the connection over to the other card and have not had any problems since. Sometimes it's just plain "broken"! :)