The issue appears to be solved. I now have 4 Yuns set up and not losing eth1 after router DHCP lease time expires.
My solution was to use the DHCP fix linked to by Sonnyyu earlier in this thread. I prefer to not set up static from the Yun side because the ethernet devices I will connect to may vary in their IP ranges.
This issue should really be publicized clearly, perhaps in "Getting Started with Yun" or similar. I realize it is an issue with OpenWRT, but the reality is that most users expect to be able to run the Yun for extended periods of time (days, weeks, months, even years) with a reliable ethernet connection.
Sonnyyu, thanks again for the help. You turned a potentially unsolvable problem for me into one that only took a few days!