WordNet (r) 3.0 (2006):

back down
    v 1: move backwards from a certain position; "The bully had to
         back down" [syn: back up, back off, back down]
    2: remove oneself from an obligation; "He bowed out when he
       heard how much work was involved" [syn: chicken out, back
       off, pull out, back down, bow out]

Moby Thesaurus II by Grady Ward, 1.0:

80 Moby Thesaurus words for "back down":
   abjure, back off, back out, backpedal, backtrack, backwater,
   balance, balk, beat a retreat, beg off, break off combat, cave in,
   cease resistance, climb down, crawfish out, cry off, debate,
   deliberate, demur, deny, disavow, disclaim, disengage, disown,
   draw back, draw off, eat crow, eat humble pie, fall back, falter,
   fear, forswear, give ground, give in, give place, give up,
   give way, go back, go back on, hang back, hem and haw, hesitate,
   hold back, hover, hum and haw, jib, move back, pause, ponder,
   pull back, pull out, quit the field, recall, recant, renege,
   renounce, repudiate, resile, retire, retract, retreat, revoke,
   run back, scruple, shilly-shally, shy, stand back, stick at,
   stickle, stop to consider, straddle the fence, strain at, swallow,
   take back, think twice about, unsay, weasel out, welsh, withdraw,
   yield