I'm getting this as well, just got a brand new PC. Tried old and new LAN drivers from both Intel's site and from gigabytes. Have tested my Ethernet connection to a laptop and it didn't disconnect once, so safe to say is not my ISP or my router or my Ethernet cable.
Windows 10 64bit
i7 6700
gtx 1070 8GB
Motherboard is Gigabyte GA-H170-D3HP
This is ridiculous.