What is JotForm?
JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
At JotForm, we want to make sure that you’re getting the online form builder help that you need. Our friendly customer support team is available 24/7.
We believe that if one user has a question, there could be more users who may have the same question. This is why many of our support forum threads are public and available to be searched and viewed. If you’d like help immediately, feel free to search for a similar question, or submit your question or concern.
I'm not sure there is actually a way to hide form from a specific user based on the fact that he submitted the form or not but, you can use 'Unique Submission' option from Preferences to prevent multiple submission by the same user.
You can set its value to cookies and IP, to ensure unique submission even if user delete or block cookies.