We use Calendly to make appointments for Cat adoption events.  People are making appointments and it appears the appointments are being cancelled the morning of by the system.  We troubleshot a few things: 

1. Made an appointment and intentionally did not cancel it on our end.  Result:  Was auto cancelled morning of.  
2. Changed the password and turned on 2 factor authentication to ensure it wasn’t a mistake on our end.  Did NOT give out any of the information and just let it sit there and did not log in at all.  Result:  appointment that we created was auto cancelled.  

I do not see anything in the settings that could do this.  The cancellations remove the event from the calendar and put the event in the trash of the email associated with the account.