What does it mean when can't get rid of persistent cough?

Depends: Need more information. How long has cough been going on, what precipitated its onset, is it productive of sputum, is it from your chest or throat, etc.? Is it accompanied by any other symptoms, has your appetite changed, do you have night sweats? See your primary care doctor and give them a full history and get examined. Good luck.

Treatment...: Treatment of a persistent cough depends on the etiologies and, there may be several etiologies present, all of which need to be treated to resolve the cough. Possible etiologies of the cough include bronchospasm from any cause, gerd, post-nasal drip. See your doctor for diagnosis and treatment. You may need testing to diagnose this cough. If you smoke, you need to quit asap!