If the External SSD is formatted FAT32, an individual file that is 4GB or larger cannot be copied due to limitations in the FAT32 file system. If you have a file that is 4GB or larger, try using a compression utility to make the file smaller. If you can compress it to less than 4GB, you will be able to copy it to a FAT32 volume.
If you do not need cross-platform compatibility for the External SSD, you can eliminate the 4GB file size constraint by reformatting the drive to NTFS (for Windows 7/Vista/XP/2000) or HFS+ (for Mac OS X).
See FAQ on “How do I reformat my External SSD or change the format type?”