Safari doesn't allow AJAX Requests after form submit?
Yes, this is how Safari and any browser based on WebKit (i.e. Google Chrome) behave. I recently ran into this on a file upload progress meter also. I ended up using the same technique seen at http://drogomir.com/blog/2008/6/30/upload-progress-script-with-safari-support to get the ajax to work. In my case, I didn't want to change the look of my application to the one Drogomir uses, but the technique itself worked. Essentially, the solution is to create a hidden iframe only in Safari that loads jQuery and your AJAX script. Then, the top frame calls a function in that frame on form submit. All other browsers still work the same as before.
Are you using an iframe to submit your form to? I'm guessing that once the form is submitted, the page enters a state where no more modifications to the DOM can be made.
Check a tutorial such as this one for more information.