Find external router IP from Arduino Yun inside router network
You can write a program that updates its own external IP every couple of minutes/hours, or when it doesn't get a response from another Yún/PC/server.

You can use this link (or find another site of the web that gives you your external IP address): http://www.realip.info/api/p/realip.php

This link has a beautifully formatted information that you can easily extract. I have a similar solution on one of my servers that have a dynamic IP...