Ubuntu Server randomly gets DHCP address instead of keeping static IP
Turns out this was a simple not having rebooted problem.
I had changed my /etc/network/interfaces to set the static interface, but never rebooted. This left dhclient running for eth1, which eventually went to renew the DHCP address. Killing dhclient fixed the problem, and with the interfaces file defining a static IP, it was not started on the next reboot.