The Collaborative International Dictionary of English v.0.48:

Undying \Un*dy"ing\, a.
   Not dying; imperishable; unending; immortal; as, the undying
   souls of men.
   [1913 Webster]

WordNet (r) 3.0 (2006):

undying
    adj 1: never dying; "his undying fame" [syn: deathless,
           undying]

Moby Thesaurus II by Grady Ward, 1.0:

39 Moby Thesaurus words for "undying":
   abiding, amaranthine, continuing, continuous, deathless, embalmed,
   ever-fresh, everlasting, fadeless, frozen, immortal, imperishable,
   impregnable, incorruptible, indefatigable, indelible,
   indestructible, ineffaceable, ineradicable, inexpugnable,
   inextinguishable, interminable, invincible, invulnerable,
   never-dying, nonperishable, persistent, quenchless, remaining,
   staying, steady, sticking, sustained, unceasing, undampable,
   undestroyable, unfading, unquenchable, unremitting