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.
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   2. To grow weak or faint with disappointment, grief, or like
      causes; to be dispirited or depressed; to languish; as,
      her spirits drooped.
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            I'll animate the soldier's drooping courage.
                                                  --Addison.
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   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]