If you have a linked image in the editor and you replace the image by clicking it to select it, opening the image manager, and inserting a new image, the link is deleted. I am pretty sure that links used to be preserved when images are replaced. i remember instructing people on how to do this regularly in templates so they did not have to recreate all the links when updating their images.
We are experiencing this issue in version: 2014.1.403.40, but as you can see the issue is reproducible in your demo site as well.
I've recorded a video using your demo site that demonstrates how to recreate this issue.
Please let me know how we can correct this, or if it's a bug when it will be fixed.