Don't believe there's a limit to FTP itself but 4G is close to the file size limit on some older *NIX filesystems (ext2 maybe?). It's entirely possible that where you're trying to send the file can't handle a file that large where you're placing it. Another possibility is that the user you're trying to copy to has quotas or other limits and that could be causing problems.

At any rate more details such as the source and destination OSes involved might shed more light.

edit: a word.