Hopeless, a. — Webster enters it under “hopeless”
1. Destitute of hope; having no expectation of good; despairing. I am a woman, friendless, hopeless. Shak.
2. Giving no ground of hope; promising nothing desirable; desperate; as, a hopeless cause. The hopelessword of "never to return" Breathe I against thee, upon pain of life. Shak.
3. Unhoped for; despaired of. [Obs.] Marston. -- Hope"less*ly, adv. -- Hope"less*ness, n.
Shades of meaning
Fernald has no entry of its own for hopelessness; he lists it under despair.
Where he writes about it:
Discouragements too frequent and long continued may produce a settled hopelessness. — from despair
Hopelessness is negative, and may result from simple apathy; despondency and despair are more emphatic and decided. — from despair