Should I have my crowned molar tooth extracted or is it worth saving?

You have two options. Have a root canal done (or redone if it's already treated) or remove the tooth. It's always best to save your natural teeth if possible. 

Sometimes this can happen and it usually doesn't cause a problem. However, in your case you have two choices, take the tooth out or endodontic therapy involving surgery. I am a bit believer in trying to save teeth if possible .

Hi:
Unfortunately without an X-ray and photo it is difficult to give you accurate advice.  Please post photo and X-ray of the area.
Best,
Dr. Maddahi

If the tooth has chronic inf croon and abscess repeatedly, I’d recommend extraction to eliminate the infection in that area permanently. If you have a broken endo file broke inside in one of your root canals, that is very challenging to repair. Prognoses very poor. Lose the tooth and plan for a bridge, partial or an implant.