The Collaborative International Dictionary of English v.0.48:

Droop \Droop\ (dr[=oo]p), v. i. [imp. & p. p. Drooped; p. pr.
   & vb. n. Drooping.] [Icel. dr[=u]pa; akin to E. drop. See
   Drop.]
   1. To hang bending downward; to sink or hang down, as an
      animal, plant, etc., from physical inability or
      exhaustion, want of nourishment, or the like. "The purple
      flowers droop." "Above her drooped a lamp." --Tennyson.
      [1913 Webster]

            I saw him ten days before he died, and observed he
            began very much to droop and languish. --Swift.
      [1913 Webster]

   2. To grow weak or faint with disappointment, grief, or like
      causes; to be dispirited or depressed; to languish; as,
      her spirits drooped.
      [1913 Webster]

            I'll animate the soldier's drooping courage.
                                                  --Addison.
      [1913 Webster]

   3. To proceed downward, or toward a close; to decline. "Then
      day drooped." --Tennyson.
      [1913 Webster]

WordNet (r) 3.0 (2006):

drooping
    adj 1: weak from exhaustion [syn: drooping, flagging]
    2: hanging down (as from exhaustion or weakness) [syn:
       drooping, droopy, sagging]
    3: having branches or flower heads that bend downward; "nodding
       daffodils"; "the pendulous branches of a weeping willow";
       "lilacs with drooping panicles of fragrant flowers" [syn:
       cernuous, drooping, nodding, pendulous, weeping]

Moby Thesaurus II by Grady Ward, 1.0:

184 Moby Thesaurus words for "drooping":
   anemic, asthenic, bagging, baggy, ballooning, bloodless,
   bowed-down, cast down, chicken, collapsing, coming apart, cowardly,
   cracking, crumbling, dangling, dashed, debilitated, decadent,
   deciduous, declining, declivitous, decurrent, degenerate, dejected,
   depressed, descendant, descending, despairing, despondent,
   desponding, deteriorating, discouraged, disheartened,
   disintegrating, dispirited, down, down-reaching, downcast,
   downcoming, downfalling, downgoing, downhearted, downhill,
   downsinking, downward, draining, droopy, dropping, dull, dwindling,
   easy, ebbing, effete, enervated, enfeebled, etiolated, fading,
   fagged, failing, faint, fainting, faintish, falling, fatigued,
   feeble, feeling faint, feeling low, flabby, flaccid, flagging,
   flapping, floppy, footsore, fragmenting, frazzled, going to pieces,
   gone, good and tired, gutless, hanging, heartless, hypochondriac,
   hypochondriacal, imbecile, impotent, in low spirits, in the depths,
   in the doldrums, in the dumps, jaded, languid, languishing,
   languorous, lax, limber, limp, listless, loose, lop, lop-eared,
   loppy, low, low-spirited, lustless, marcescent, marrowless,
   nerveless, nodding, on the descendant, on the downgrade,
   pessimistic, pining, pithless, plummeting, plunging, pooped,
   powerless, ready to drop, regressive, relaxed, retrograde,
   retrogressive, rickety, rubbery, run ragged, run-down, sagging,
   sagging in folds, saggy, sapless, seedy, setting, shaky,
   shriveling, sinewless, sinking, slack, sliding, slipping, sloppy,
   slumping, soft, spineless, spiritless, streaming, strengthless,
   subdued, submerging, subsiding, suicidal, swag, tabetic, tired,
   tired-winged, toilworn, tottering, tumbledown, unhardened,
   unnerved, unrefreshed, unrestored, unstrung, waning, wasting,
   way-weary, wayworn, weak, weakened, weakly, wearied, weariful,
   weary, weary of life, weary-footed, weary-laden, weary-winged,
   weary-worn, wilting, withering, woebegone, world-weary, worn,
   worn-down, worsening