I noticed this about a year ago, and wrote a small tool that I use to keep my own links "fresh" over time. Instead of linking directly to Amazon I link to my own domain. It acts as a redirect to Amazon itself, which allows me to update the links in posts that I've made months ago, even if the site where I made those posts doesn't allow it. I've also got a script that I can use to identify when links no longer point to the products I intended and alerts me so I have a chance to update them.
Keeping this system of mine up-to-date isn't a huge task, but I'm wondering if there is someone offering this sort of thing as a service?