Perspiration, oils, and invisible residue on the copper contacts are the most common reason a watch stops charging, even with a brand-new cable. Use a cotton swab lightly dampened with rubbing alcohol (or a dry microfiber cloth) to thoroughly clean the charging pins on the back of the watch.
Let it air dry completely for about 2 minutes before reconnecting the charger, and make sure the watch is seated with the metal contacts aligned directly to the base.