I found a solution for my Gigabyte G1.Sniper.M3 and Windows 8 x64:
1. flashed modified BIOS found here Z77 Modified Bios
2. updated Intel ME driver found here Intel ME 8: Management Engine Driver
3. updated Intel 82579L driver found here: Intel Network Adapter Driver for Windows 8
No more connection drop problems. It looks like the whole problem is related to Intel Management engine.