CentOS not detecting Intel 10G (ixgbe) interface

This actually looks like a problem with your server's motherboard.

We can see from your dmesg output that it is failing to communicate correctly with the PCIe card in the failing server, but works correctly in a different server.

So you most likely have a bad PCIe slot, or bad motherboard components.

You can try using a different PCIe slot, if you have another one available, checking that your NIC and riser card (if any) are firmly seated, or replacing the riser card or motherboard.

It could also be, if you haven't actually tried this specific NIC in a different server and had it work, that the NIC itself is bad.

Try ifconfig eth2 up.

I seem to recall having to do that to get the interface seen.