Hi Mary,
The only way a lead can receive another invite email is if their program status remains "Invited" at the time the email send step is executed in your flow. I can see that you have a wait period with a specific date and time.
Is it possible that you forgot to set this to a future date and time for your test? If you didn't have a future date/time set, I think it would negate the wait step.
The other thing to check, is that your smart campaign "02b.Registered" is changing the program status from "Invited" to "Registered" when you fill out the form.
I hope this helps you troubleshoot the issue.
-Nate