Hi there @DrJ428 ,
Thanks for reaching out to us on the Instructure Community!
Deleting your student from the course does not delete their account. Deleting their account to allow them to try again requires assistance from the employees at Instructure that are the administrators of Free for Teacher. I also don't recommend signing up a second account as a student, either, as that can cause issues with enrollments, especially if you use the same email twice.
What your student should do is open the log in screen and click 'Forgot Password'. They should then enter the email that is associated with the account that they created initially, and then DOUBLE CLICK the 'next' button. Double clicking is required for the email to get pushed to the user's inbox, the reason for this is unknown.
If you still require more assistance, please reach back out here and let us know. We're happy to help you!