I'm guessing that you are talking about a PDF form (and not a web form), right?
With the Web form you can use the redirect to go back to the empty form after a submit (paid subscription only).
For the PDF forms I think this is a bit more complicated. You might be able to add script to the PDF to disable the save button... or can you just not make the file readonly on that system? This would preventing people from saving over it? You would have more luck asking the http://forums.adobe.com/community/acrobat forum. Note that you will need to remove the Reader Extention to do these steps (which includes File > Save a Copy... and open the saved copy before you can flatten the form fields).