Just tried that link and got an error-

Internal Server Error

The server encountered an internal error or misconfiguration and was unable to complete your request.

Please contact the server administrator, webmaster@lynmilner.id-ia.net and inform them of the time the error occurred, and anything you might have done that may have caused the error.

More information about this error may be available in the server error log.

Additionally, a 500 Internal Server Error error was encountered while trying to use an ErrorDocument to handle the request.

Have you done something since posting your question?

Have you tried clearing your cache under 'Sitewide Settings'? Also.. if the images are in file-sets, check to make sure they are set to 'Public'.

I can still access the site and a hard refresh does not seem to affect it.

Strange, I can see alot of them are being pulled from the cache you could try clearing that to check but I would check the file locations.

according to the inspector you are actually missing the files from your remote directory,

http://lynmilner.com/concrete/themes/default/images/nav_horizontal_...

I would check to make sure your domain is correct and that is should not behttp://www.(should not make a difference)

If the files are on the remote server, I would check your .htaccess file and make sure something is not redirecting those files

The images you see in the filemanager could be cached thumbnails so check if you can actually view them? and then match the URL location with the live site.

Check that the permissions of the files are set to allow public access and you client has not been playing with the only allow users to view "Own images"

My guess is its a redirection/Permissions problem failing that if the files are actually missing from the remote then it suggests the files have been removed/moved

delete your .htaccess file and see if that has any effect.