As soon as an appointment status has been set to cancelled by an end user, the user cannot set it back to any other statues.
The only way that you could reopen cancelled appointments is via the data workbench. You export the appointments. In the downloaded file you change th status (from 4 to 1 for example). Via the import function [Individual object], [Update], you select your file, upload the file and then overwrite the statusses.