Thank you. The default app that downloads to when the client joins an attended session is not designed to stay on the computer permanently, so I suspect the one you are using is automatically removing itself.
This support article explains how to install a modified version of the Unattended Support app: How to install and use the app. After you run the installer it will stay on the computer (until uninstalled), and add an icon to the tool bar which the user can click on and select Join a session, bypassing the need to go to fastsupport.com