Unable to import an external site into our multisite environment - Failed to import Media

We have a multisite setup with several sites all working smoothly. I have another site that is currently running on a stand alone version of WordPress. Both sites are running WordPress 3.6.1.

I exported the stand alone site (creating the WXR XML file), imported it into a newly created multisite site and checked the box to download and import file attachments. I then get a page full of "Failed to import Media" error messages for all the attachments. I have turned on debugging for the importer and for each file it says "Remote server did not respond".

I have looked in the XML file and tried to navigate to one of the file attachments. This works successfully so I know the file locations are working. I have checked the file structure for the new multisite and it seems as though the upload folders are being created, however the files aren't being downloaded.

Does anyone know what the issue could be? Perhaps it's a security/permissions issue? I've changed the permissions on the site's upload folder to 777.

I have seen other forum posts with users having the same issue when they upgraded from WP 3.5.1 to 3.5.2. We're using 3.6.1 so I would figure this maybe some kind of permanent code change somewhere?

Any help much appreciated. Thanks.