Sorry about hijacking your post. I thought you were having the issue with the 7.0 version and losing your external NIC.
Just a few things I have seen on other posts and look for are as follows:
1. Is the network running. I don't recall any good way of doing from the server-manager in 5.6. I would open a telnet or ssh connection to the server using putty, do a "/etc/rd.d/init.d/networking status" (might want to check the directory to see if it's networking or network - I just type in netw and hit the tab) I'm pretty sure that the rc.d directory is still used in 5.6. This status tells you if the network deamon running. If so, check the NICs.
2. Are the NIC's found and running. From the telnet or ssh connection to the server using putty, do a "/etc/rd.d/init.d/ifconfig" This tells you if the network cards are running as well as their static IP addresses, dropped packets, errors, etc.. If your having a problem seeing it all, add a " |more" (skip the " marks) after the ifconfig so it limits the screen to a page so you can read the first NIC. This should tell you if they are running. You would see and eth0, eth1 and lo.
3. If you look in the /var/log/dmesg log, it may tell you if your hardware is being found and running.
My experience is that the 5.6 version has always worked well for me, however, I've always used matching NICs, as recommended and knock on wood, not had one die.
Another thing to check is if the motherboard has an on-board NIC and to disable it in the BIOS if you're not using it. If they all use the same driver, you might not know it's doing anything to you without seeing how many eth's you have. The ifconfig would give you a hint if you see an eth2.
Hope this helps and that someone who may have seen a problem with the 5.6 version can add more info and sorry about stealing your post. Unfortunately, my bet would be that Charlie Brady was the best bet for figuring it out since he's one of the more kowedgeable folks on SME.
Might want to also do the "netstat -i" and post as Charlie asked to see if my cards are transmitting and receiving, but it's your cards that may be having an issue. netstat -i gives similar information as the ifconfig command, but in table format.