The run tree is a volatile structure populated at runtime and as such any changes will be lost on reboot.
exFAT filesystems does implement permissions nor does NTFS on Linux.
You partition label/UUID indicates a foreign filesystem.
If the device is NTFS it can be due to an error in the filesystem or you are dual booting a Windows system with Windows fast boot and or hybrid sleep enabled.
Fix this by booting into Windows and use Windows to check the file system - also use power management to disable the mentioned features.
Please use this guide to create a permanent mount point for your device.