Some ftp servers limit how many files will display as the result of an "ls" command. This is to limit the possbility of DOS attacks, I suppose.
If you have more than 2,000 files on your website, or in a specific directory, this can be problematic. No matter whitch FTP client you use, you'll be limited by this setting. The real fix is to edit the server configuration, or ask you hosting provider to do so. Otherwise, you can try a few workarounds, if you are trying to download all the files:
If you have shell access, login and just "tar -cvf file.tar directory_with_lots_of_files" - this should work and will create 1 file you can download for a backup.
Using ftp, try to "mget x*", where "x" is a pattern that some files have. If the result is less than 2,000, you can try a few different patterns (if you know all the filenames in the directory) to eventually download all the files.
By the way, before using mget, turn off the prompting by issuing a "prompt" command. Otherwise, you'll have to answer "Y" to every single file being downloaded.