"despondent condition, a sinking or dejection of spirit from loss of hope or courage in affliction or difficulty," 1670s, from Latin despondentem (nominative despondens), present participle of despondere "to give up, lose, lose heart, resign," also "to promise in marriage" (especially in phrase animam despondere, literally "give up one's soul"), etymologically "to promise to give something away," from de "away" (see de-) + spondere "to promise" (see sponsor (n.)).

Despondency is a loss of hope sufficient to produce a loss of courage and a disposition to relax or relinquish effort, the despondent person tending to sink into spiritless inaction. Despair means a total loss of hope; despondency does not. [Century Dictionary, 1897]

"lack or loss of compensation," especially, in medicine, "deterioration of a structure that had worked through compensation," 1900, from de- + compensation.

mid-15c., indempnite, "security or exemption against damage, loss, etc.," from Old French indemnité (14c.), from Late Latin indemnitatem (nominative indemnitas) "security for damage," from Latin indemnis "unhurt, undamaged," from in- "not, opposite of, without" (see in- (1)) + damnum "damage" (see damn). Meaning "legal exemption" is from 1640s; sense of "compensation for loss" is from 1793. Related: Indemnitor; indemnitee.