I am not sure why the NIC disappears in the network connections. This might be some sort of resource issue in the system. If that is the case, then you might be able to turn off some features in the BIOS that could make the problem disappear. Another thing to look at would be to make sure you have the latest BIOS version.
Another area I would look at is some sort of interaction with security software, especially software that adds virtual NICs to the stack. For that matter, any software that adds something to the networking stack would be a place to investigate. Sometimes the installation order can make a difference. For example, you could install and configure the network connections first and then install the other software.
Neither of the ideas are based on any specific issues where the connections disappeared, but these are areas I would look at. I hope someone else might have some thoughts on this issue.
you can also try updating your driver to version 9.13.x.x since in your signature you mentioned 9.12. two ways to update your driver:
using Intel driver update utilty or download the driver from the site
you can find both driver update utilty and driver files in this site - http://downloadcenter.intel.com/Default.aspx