Previously uploaded images now appear broken

I run the blog privateequitykorea.com for work. It was recently brought to my attention that the majority of images that were uploaded before are broken. When I look at the image gallery associated with each post, the images are there and I can re-insert them into the post and they appear fine but the link for each image no longer works.

Given the large amount of images that would need to be fixed, I’d rather not reformat each post by hand. Is there a way to fix this problem all at once? I haven’t made any changes that I can think of causing this. Any ideas?