1866, of persons, "to have the health or strength reduced," from the verbal phrase; see run (v.) + down (adv.). From 1896 of places, "dilapidated, shabby, seedy;" by 1894 of clocks, etc., "completely unwound." The earliest sense is "oppressed" (1680s). Compare rundown (n.).
The verbal phrase run down as "have the motive power exhausted" (of clocks, etc.) is by 1761; of persons, etc., "become weak or exhausted," by 1828. To run (something or someone) down "disparage, abuse" is by 1660s.
late 15c., earlier upsadoun (late 14c.), up so down (c. 1300); the so perhaps meaning "as if." As an adjective from 1866.