I have almost the same hardware, except an Intel CPU rather than the AMD, Windows 7 Home Premium, and am experiencing the same problem. Windows reports that the installed NIC driver is a Broadcom NetLink Gigabit Ethernet, and repeated attempts to update the driver with something newer end up unsuccessful with Windows telling me that the driver I have installed is the most current. I unchecked the option to allow Windows to manage the power settings on the NIC more than a month ago, and I still have the intermittent drop in connectivity.
Every time my connection drops, I get an event in the System Event Log talking about "Name resolution for the name x.domain.whatever timed out after none of the configured DNS servers responded." Invariably, I must then reboot the machine to get the NIC back. Performing a Windows repair on the adapter results in much thinking, but ultimately no solution. Also, an attempt to manually disable and re-enable the adapter after this happens causes my machine to hang, then BSOD with a power related error (don't have it verbatim at the moment).
Basically, the connection randomly drops, seemingly more often when returning to the computer after a period of inactivity, and it doesn't come back without a reboot. This is HIGHLY annoying, and although all the potential solutions I've seen talk about turning off power management or disabling AVG anti-virus, they haven't resolved the problem for me.
If I do find a solution, I'll return to this thread with an update.