How can I loop this form so it reappears after someone signs in?

If you would like for the form to reload after each submission, rather than showing a thank you page, you can set your thank you page URL to the same URL as your form:

https://www.jotform.com/help/211-Setting-Up-the-Thank-You-Page

This will reload the form each time the form is submitted.

If there is something else  you are looking for, please let us know a bit more detail regarding your requirements and we will be happy to help.