Comment 4 for bug 991666

I believe I have found what was casuing the problem in my case. I have a Realtek R8168 onboard ethernet, but Ubuntu was loading the Realtek R8169 driver.

lspci | grep -i eth output:

01:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8111/8168B PCI Express Gigabit Ethernet controller (rev 06)

I followed the instructions here to download and install the proprietary Realtek 8168 drivers:

http://amk1.wordpress.com/2009/06/09/realtek-8168-module-issue/

It's still too soon to know for sure, but so far my VPN connection has been up for over 2 hours (longest it has ever been up without dropping).