It sounds like a server issue to me. I don't see how it can be something that InDesign would cause.
How do you move it? With the Finder? Inside of InDesign?
Does it happen with other files or only .indd files?
Lastly, are you moving the .indd files and breaking the links to the images? If so, we'll go through that with you.
If you are packaging the file inside of InDesign and moving the new folder, then yes, packaging creates a copy and pulls the links into the new folder.
What applies from all that I threw out?