The Collaborative International Dictionary of English v.0.48:

Totter \Tot"ter\, v. i. [imp. & p. p. Tottered; p. pr. & vb.
   n. Tottering.] [Probably for older tolter; cf. AS.
   tealtrian to totter, vacillate. Cf.Tilt to incline,
   Toddle, Tottle, Totty.]
   1. To shake so as to threaten a fall; to vacillate; to be
      unsteady; to stagger; as, an old man totters with age. "As
      a bowing wall shall ye be, and as a tottering fence."
      --Ps. lxii. 3.
      [1913 Webster]

   2. To shake; to reel; to lean; to waver.
      [1913 Webster]

            Troy nods from high, and totters to her fall.
                                                  --Dryden.
      [1913 Webster]

WordNet (r) 3.0 (2006):

tottering
    adj 1: unsteady in gait as from infirmity or old age; "a
           tottering skeleton of a horse"; "a tottery old man" [syn:
           tottering, tottery]
    2: (of structures or institutions) having lost stability;
       failing or on the point of collapse; "a tottering empire"