File is too large for destination file system - Already NTFS

This is my first SuperUser post, so please bear with me if I make any mistakes, thanks.

I have some large database files (4-7GB) that I need to transfer to an external hard drive (WD My Book, 6TB). However, when attempting to copy the files to the hard drive, I receive the error that says The file '[my filename]' is too large for the destination file system and have to abandon the copying process. This is very annoying because I am copying from a server across an internet connection, and the copying process runs for 4+ hours before I receive the error.

EDIT: Just for clarification/details, the error has shown for at least 5 different files attempted so far.

UPDATE: As suggested, I tried copying one of the large files to my internal hard drive. This also resulted in the same error message, and my internal hard drive is also NTFS. It would appear that the external hard drive is not causing the error.

The frustrating thing is that every help topic I can find says to convert the external hard drive's FAT32 system to NTFS, but my external hard drive is already an NTFS file system.

Why does my NTFS hard drive throw maximum file size errors, and what can I do?

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I am using Windows 7 Professional, 64-bit, 8GB RAM

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UPDATE: Per suggestions, I tried to copy the files using robocopy, but it failed for the large files both to the external drive and to my local machine. There is an error message:

ERROR 87 (0x00000057) Copying File [my filepath]\[my filename] The parameter is incorrect.

There were smaller files that successfully copied, but it failed at 90.3% of a 4.4GB file. The robocopy command that I used was as simple as I could make it (it's my first time using it):

robocopy "[my filepath] " "[my destination path] "

So, an example with the company path names changed: robocopy "J:\Top Folder\Sub Folder\Originating Folder " "\\Client\C$\Users\doejohn\Documents\Top Folder\Destination Folder "

It seems to be something related to 4GB; but, unless I'm just flat missing something, both the external drive and my local disk are NTFS (I right-click on the drive in Explorer and go to properties, the General tab shows information about used and free space, the file system says NTFS).

So, after a lot more searching (I find it difficult to locate help for specific Citrix issues), I found a Citrix help page that actually describes my issue: http://support.citrix.com/article/CTX134844. It is specifically a Citrix issue, unfortunately, and the page does not provide a solution.

As some of you noted, the magic cutoff size is 4GB, and this is just a limitation of the XenApp service we are using, regardless of the file systems in place-- the error message is not accurate.

In order to copy these large files, I believe that I will need to find some other service (like a cloud storage location) or gain physical access to the server and copy the files to an external drive there.

Thank you to everyone that helped me troubleshoot this frustrating and time-consuming problem!