How would a program on your PC know there is a new file to upload if the site isn't checked regularly?
All you can do: write a program that get the index page (just some html or output from a dir in ftp), parse it and compare the current set of files with the previous one the program stored in its database. Then, if new ones are found it, download it to a specified location.
That's an interesting programming task. I doubt if such a program already exists, but it surely can be written. If you need it, either do it yourself, or pay somebody to do it for you.
Is there a program which would allows users to automatically download files as soon as they are uploaded to a particular website , without the need of checking the website itself ?