early 14c., "deterioration, degeneration, a sinking into an impaired or inferior condition," from Old French declin, from decliner "to sink, decline, degenerate" (see decline (v.)). Meaning "the time of life when physical and mental powers are failing" is short for decline of life (by 1711).
"to support or prevent from falling by placing something under or against," mid-15c., probably from prop (n.1) or a related verb in Dutch. Meaning "support or sustain" in a general sense (especially a cause, institution, etc. at risk of failing) is from 1540s. Related: Propped; propping.