Hello Casper,
Invitations are send once a day at 2 different moments, either if you open the testimonials component via the backend or via the front-end.
Whether or not invitations are send depends on your settings. These are the Reminder settings. The order must be older than x days and have status Y and no reminder for that order has been sent before, that is when the reminders are sent.
If the sending procedure has already been executed within the last 24 hours, it won't do it again. If you want to repeatedly fire the sending procedure you can change the column reminder_last_check in the jd_testimonials_settings table to 0.