Seems that at least I relized what is Your problem. I was talking about fully functional TC installed on the flash drive. But You use the CD image copied to flash drive, such image is not fully functional, it assumes that media is not writeable, this is why Your saves go to nowhere.
So now You have the flash drive with the CD image copied on it. Yoe need to boot from it, and install TC on another flash drive. And those second drive will be the fully functional TC installation.
If You start with Xvesa desktop, there is an icon TCInstall, which is what You need. Or run
sudo tc-install.sh
from the command line.