Files not found by iTunes

We've been running into an issue where our xml files will not refresh in the Public Site Manager. We receive error messages like this one:

We also error messages like this one when we try to upload a new collection:

This has been happening on multiple collections (not just one). Each time we try to refresh, a different audio/video file is shown as missing. So for the screenshot above, the next time we try to add that feed, it might be "smh_019.m4v" or "smh_007.m4v" that is missing. We haven't found a pattern for the audio/video files that are supposedly missing.

The files are definitely on our server in the correct location (we can reach them by typing the url directly into our browser). We also have validated our XML files using multiple feed validators.

This issue happened about a year ago, and one day it just went away, and uploading/refreshing went back to normal. It was working properly until about a month or so ago, and we began getting these same error messages again.