Hi Larry,
I recommend to test after your first highlights if they got saved.
Saving highlights works for thousands of users. Why it doesn't work for you can have tons of reasons (i.e. wrong OS, wrong usage or simply that you did highlights on a page that constantly changes its content). Therefore I also recommend to read the instructions first and in case of problems ask the developer for help (per email or by opening an issue on GitHub).

EDIT :-) Also keep in mind that Textmarker might not be able to restore your highlights in case the corresponsing page's content changes before your next visit. Address for issues/bugs/feature requests: https://github.com/ufb/Textmarker/issues