Faça o download do driver oficial do realtek.
Em seguida, remova o módulo r8169 do kernel do Linux.
# rmmod r8169
<Quick install with proper kernel settings>
Unpack the tarball :
# tar vjxf r8168-8.aaa.bb.tar.bz2
Change to the directory:
# cd r8168-8.aaa.bb
If you are running the target kernel, then you should be able to do :
# ./autorun.sh (as root or with sudo)
You can check whether the driver is loaded by using following commands.
# lsmod | grep r8168
# ifconfig -a
If there is a device name, ethX, shown on the monitor, the linux
driver is loaded. Then, you can use the following command to activate
the ethX.
# ifconfig ethX up
Por fim, na lista negra do driver r8169, inclua o seguinte em /etc/modprobe.d/blacklist.conf:
#blacklist r8169 driver
blacklist r8169
Encontrei em link e funciona. Agora está tudo bem com a velocidade da rede.