Earlier, I failed to find some information relevant to my problem. The following link describes my symptoms to a tee, but with the RTL8102EL device.
https://bugs.launchpad.net/ubuntu/+source/linux/+bug/240470 Here's one more specific to the RTL8111: http://aplawrence.com/Linux/rtl811.html In any case, it looks like the answer is to: 1.) Download the latest rtl8168/rtl8111 source from Realtek. 2.) Boot into 2.6.32-5-amd64. 3.) Build the driver module. 4.) Remove the r8169.ko module from /lib/modules/2.6.32-5-amd64. 5.) Run depmod. 6.) Run update-initramfs -u -k 2.6.32-5-amd64. 7.) Reboot into 2.6.32-5-xen-amd64 and repeat steps 3-6. 8.) Reboot back into Xen, network's up and running. So far, no issues with the updated config.