The r8169 driver has been a problem for a long time. Realtek is kinda dutty with linux. I am having issues with my realtek soundcard at the moment. The drivers always need some stupid tweak. For me the tweak breaks linuxmce 1204.
anyway for your situation try the r8168 driver. and blacklist the 8169 driver. this will most likely break something but its worth a shot. I would first try and blacklist the r8169 driver and reboot. Then try what is below.
# download driver for r8168, and unpackhttp://www.realtek.com.tw/downloads/...&getdown=false
# go to driver location
sudo rmmod r8169
sudo mv /lib/modules/`uname -r`/kernel/drivers/net/r8169.ko ~/r8169.ko.backup
make clean modules
sudo make install
sudo depmod -a
sudo insmod ./src/r8168.ko
sudo mv /initrd.img ~/initrd.img.backup
sudo mkinitramfs -o /boot/initrd.img-`uname -r` `uname -r`
sudo echo "r8168" >> sudo /etc/modules