wear down
1. To remove or disappear little by little through use, time, or the action of weather.
Time and weather have worn off the name on the gravestone.
The eraser has worn off my pencil.
The grass has worn away from the path near the house.
2. To lessen; become less little by little.
The people went home as the excitement of the fire wore off.
John could feel the pain again as the dentist's medicine wore away.
3. To exhaust; tire out, win over or persuade by making tired.
Mary wore her mother down by begging so that she let Mary go to the movies.
Compare: DIE OUT.
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Source: A Dictionary of American Idioms