I have the same NIC on a ASUS P8Z68 Deluxe.
I recently updated my Intel NIC driver to 18.3 and started getting e1cexpress, Event ID 27, Network link is disconnected issues. I ran the 82579VSKUW64e in command prompt and it said no update needed.
I uninstalled 18.3 and went back to my old 16.8.1 driver and the errors stopped appearing in Event Viewer. I'm pretty sure it's a driver related issue at this point.
I noticed that 18.5 is available on Download Center, has anyone tried 18.5?