The Collaborative International Dictionary of English v.0.48:

Sag \Sag\ (s[a^]g), v. i. [imp. & p. p. Sagged; p. pr. & vb.
   n. Sagging.] [Akin to Sw. sacka to settle, sink down, LG.
   sacken, D. zakken. Cf. Sink, v. i.]
   1. To sink, in the middle, by its weight or under applied
      pressure, below a horizontal line or plane; as, a line or
      cable supported by its ends sags, though tightly drawn;
      the floor of a room sags; hence, to lean, give way, or
      settle from a vertical position; as, a building may sag
      one way or another; a door sags on its hinges.
      [1913 Webster]

   2. Fig.: To lose firmness or elasticity; to sink; to droop;
      to flag; to bend; to yield, as the mind or spirits, under
      the pressure of care, trouble, doubt, or the like; to be
      unsettled or unbalanced. [R.]
      [1913 Webster]

            The mind I sway by, and the heart I bear,
            Shall never sag with doubt nor shake with fear.
                                                  --Shak.
      [1913 Webster]

   3. To loiter in walking; to idle along; to drag or droop
      heavily.
      [1913 Webster]

   To sag to leeward (Naut.), to make much leeway by reason of
      the wind, sea, or current; to drift to leeward; -- said of
      a vessel. --Totten.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Sagging \Sag"ging\, n.
   A bending or sinking between the ends of a thing, in
   consequence of its own, or an imposed, weight; an arching
   downward in the middle, as of a ship after straining. Cf.
   Hogging.
   [1913 Webster]

WordNet (r) 3.0 (2006):

sagging
    adj 1: hanging down (as from exhaustion or weakness) [syn:
           drooping, droopy, sagging]

Moby Thesaurus II by Grady Ward, 1.0:

111 Moby Thesaurus words for "sagging":
   abatement, abridgment, alleviation, attenuation, bagging, baggy,
   ballooning, collapsing, contraction, dampening, damping,
   debilitated, deciduous, declining, declivitous, decrease,
   decrement, decrescence, decurrent, deduction, deflation,
   depreciation, depression, descendant, descending, diminishment,
   diminution, down, down-reaching, downcoming, downfalling,
   downgoing, downhill, downsinking, downward, drooping, droopy,
   dropping, dying, dying off, enervated, enfeebled, extenuation,
   fade-out, fagged, faint, fainting, falling, fatigued,
   feeling faint, flagging, floppy, footsore, frazzled,
   good and tired, jaded, languid, languishment, lessening, letup,
   limp, loose, lop, lop-eared, loppy, lowering, miniaturization,
   mitigation, nodding, on the descendant, on the downgrade,
   plummeting, plunging, ready to drop, reduction, relaxation,
   run ragged, run-down, sagging in folds, saggy, scaling down, seedy,
   setting, simplicity, sinking, submerging, subsiding, subtraction,
   swag, tired, tired-winged, toilworn, tottering, tumbledown,
   unrefreshed, unrestored, way-weary, wayworn, weak, weakened,
   weakening, wearied, weariful, weary, weary-footed, weary-laden,
   weary-winged, weary-worn, wilting, worn, worn-down