The life in my old Garmin Edge 205 is very short, is it worth replacing the battery or just buy a new model?

I have had it for a good few years and its been used a lot.

Replace, unless you have the skill to do it yourself.
Aldi were/are doing Garmin 200 for £40-£50, or you could just get a second hand gps.

I replaced the battery in mine before passing it on to my niece. So long as your happy using a soldering iron it was pretty easy to do. I googled a how to guide and just followed that.