Strange problem indeed! The first thing that comes to mind is maximum file sizes related to the type of formatting on your drive. It might be the wrong approach but if you have another external drive or a large enough USB stick, you could try copying to that instead and see if that gets you the same results. If that fails too, check the type of format on the various drives (ie. FAT32 or NTFS etc.) If the format of the source and destination drive is the same then we'll have to look elsewhere.
Another thing to try is plugging the external drive in another USB port, preferably one that's directly on the system's mainboard. That would eliminate issues with dodgy USB hubs.