I humbly submit the following idea for your consideration:

1. Click on link to go to form, and they go to a page asking for username/password (or other authenticating tokens) (and advises that the site uses cookes you'll see why in a moment.
2. Submitting username/password form checks against a database (be it full-blown database, or text file, or whatever).
3. Set a cookie in their browser if successful, then refer/redirect them to the form page.
4. If cookie is set, display form; otherwise, display an "access unavailable" message.
5. Optionally, update the/another cookie with the number of times they have submitted, which can be checked against the maximum number of times you wish to allow them to submit.

I am sure there are more experienced monks here who may offer better/easier solutions. Good luck with your project.