Please do a man on the tar command. Specifcally the -T option and the -X option.
You can even use google, bing, duck duck go, yahoo. It is not rocket science. It is not unique to Tiny Core.
Hint. -T uses /opt/.filetool.lst -X uses /opt/.xfiletool.lst
Simple basic file managment. Static content should not be included in backup but should be a candidate for a personal extension or stored on other persistent store.
This procedure has been in public use for 8 years across two distributions and is covered in the Core Concepts document.
Persistent does not fail unless caused by user error in not understanding the basics involved.