On what filesystem are you storing the file? A Fat32 filesystem has a 2 GB limit. Also, using smb there is a 2 gb limit as well. ( The windows networking protocol ). For something that large, I would use either the wget program with the continue option or use a bit torrent client. An ftp client might be a better as well. For the latter 2 options, the site you are downloading from would need to offer the service. For wget, you could use the same url that you used with firefox. (wget is a linux console program. However you may be able to compile it for windows as well, or maybe you can find it for windows.)
It's also possible that firefox uses 32 bit integers internally to track filesizes. Since it is open source you could check that for yourself.