I had troubles with the Ubuntu
r8169 driver and my Realtek RTL8111/8168B PCI Express Gigabit Ethernet controller for a long time.
Finally it semms that I found a solution for a stable ethernet connections: The new r8168 driver (Version 8.031.00 - found here) seems to work quite good out of the box.
Just extract it, and run autorun.sh (as root)
# sh autorun.sh
Of course, you have to do this after a kernel update once again. Don’t forget this - It frakked me one time!
Thats all :-)