Despondency, n.
The state of desponding; loss of hope and cessation of effort; discouragement; depression or dejection of the mind. The unhappy prince seemed, during some days, to be sunk in despondency. Macaulay.
Shades of meaning
Fernald has no entry of its own for despondency; he lists it under despair.
Where he writes about it:
Hopelessness is negative, and may result from simple apathy; despondency and despair are more emphatic and decided. — from despair
Despondency is an incapacity for the present exercise of hope; despair is the utter abandonment of hope. — from despair
Despondency relaxes energy and effort and is always attended with sadness or distress; despair may produce a stony calmness, or it may lead to desperation. — from despair