I have not researched your issue in particular, so I do not know if these thoughts will help or not.
I see the latest driver is dated 10/14/2011, version 18.104.22.168. That driver was part of Intel(R) Network Connections version 16.7.
What version driver and network connections software is installed? Did you upgrade the network connection software recently? You might want to try uninstalling the software and installing an earlier version if the complaints coincided with an update. You might want to try whatever version ASUS has posted for your server board.
On the other hand, if you have not updated the network connection software or driver, then you might want to give the latest version a try. You can download the latest software and drivers from http://downloadcenter.intel.com/Detail_Desc.aspx?agr=Y&DwnldID=18719.
You might also find that the issue has some external cause. I have seen some weird causes of network disconnections over the years. For example, you might have some change on the link partner (switch?) side of the connection that is behind the change.
Some other resource change on the server or a physical issue might behind the issue too. Have you updated some piece of software? Was their a major update to the security software? Was their a change in the physical routing of the cable?
Have you added a new plug-in adapter? I have seen weird things happen because of power supplies that were aging or on the edge. You could have a case where the power has become marginal for just one of the voltages from the supply because of adding a device to the server or because of aging components.
For that matter, sometimes component damage caused by static electricity or some type of dip or surge might not manifest itself until well after the event. Internal damage of this type would not be evident by looking.
Or you might have had some completely unrelated piece of equipment that is now causing you a problem. I recall an example of a server from many years ago that used to go down when an industrial oven on the other side of the wall was started. Apparently, the electrical field from the oven was making the UPS shut down the server because of a probem with the power. My point is that if you cannot find the problem with the obvious fixes, don't rule out anything in the vicinity.
I would be interested in hearing about whatever you find.