Power management is cutting power to the Intel 82579LM NIC. Fix: Open Device Manager → Network adapters → Intel 82579LM → Properties → Power Management → Uncheck “Allow the computer to turn off this device.” Also, download the latest Intel PROSet driver (v25.5 or newer, still compatible).
LGA 1155, supporting 2nd Generation Intel Core i3, i5, and i7 processors (Sandy Bridge, 32nm). Lenovo Is6xm Rev 1.0 Motherboard Drivers