Some things you can try:
Make sure you have the latest driver in for the onboard Ethernet
Try setting its maximum speed to 100mb or ever 10mb. To test for stability.
Put the latest BIOS in the mobo, especially as the LAN is onboard.
Care must be taken with that.
If I suspected the on board Ethernet I would disable it in the BIOS and try a pci card in there.
I can’t think of anything else at the moment, but that forum I linked to is a good one, you don’t have to be an overclocker like me [

] to ask for help and there are a lot of people who really know their stuff on it.