The work around is shorter than this blog entry title:
Clear the Amazon AppStore cache/data.
Start by closing the app that is giving you that message. Then force close the Amazon AppStore app, followed by clearing the data/cache for it. Finally, launch the Amazon AppStore and login again, choosing to reenable/disable settings as appropriate (in-app purchases, etc).
Now you can go offline and enjoy your AppStore purchases without being prompted for an Internet connection (for apps that do not truly require it).