down
to make sb/sth weaker or less determined, especially by continuously attacking or putting pressure on them or it over a period of time :
Her persistence paid off and she eventually wore me down.
WEAR SB/STH
Meaning of WEAR SB/STH in English
Oxford Advanced Learner's English Dictionary. Оксфордский английский словарь для изучающик язык на продвинутом уровне. 2005