The Collaborative International Dictionary of English v.0.48:

Despondence \De*spond"ence\, n.
   Despondency.
   [1913 Webster]

         The people, when once infected, lose their relish for
         happiness [and] saunter about with looks of
         despondence.                             --Goldsmith.
   [1913 Webster]

WordNet (r) 3.0 (2006):

despondence
    n 1: feeling downcast and disheartened and hopeless [syn:
         despondency, despondence, heartsickness,
         disconsolateness]