My experience with lithium ion batteries over the past 10 years indicates that using them wears them out. If you fully drain and discharge them daily, they'll last 1-2 years before they're down to 50% or less. If you rarely drain them (i.e., keep them plugged in all the time), they'll keep say about 80% of capacity for 5+ years. The discharge/recharge is effectively a destructive process.
This is based on my experience with Lithium Ion batteries on my Dell laptops. The Lithium Ion Polymer batteries used in the eDGe I believe is basically the same, merely lighter and more easily molded into custom shapes. If someone knows different regarding polymer, I'd be interested to hear from you
So, my recommendation is to keep it plugged in as much as you can and drain the battery as little as you can - without killing yourself with inconvenience of course.
EDIT: Based on some further digging I did in a post below, and being reminded by a post by dontpanic, it seems that it doesn't really matter how much or how little you run on battery, it will last at least 4 years. (The User Guide (click the Help app) has some battery care tips with regards to temperature, though.)