The Collaborative International Dictionary of English v.0.48:

Inextinguishable \In`ex*tin"guish*a*ble\, a.
   Not capable of being extinguished; extinguishable;
   unquenchable; as, inextinguishable flame, light, thirst,
   desire, feuds. "Inextinguishable rage." --Milton.
   [1913 Webster]

WordNet (r) 3.0 (2006):

inextinguishable
    adj 1: difficult or impossible to extinguish; "an
           inextinguishable flame"; "an inextinguishable faith"
           [ant: extinguishable]

Moby Thesaurus II by Grady Ward, 1.0:

23 Moby Thesaurus words for "inextinguishable":
   deathless, enduring, eternal, everlasting, immortal, imperishable,
   impregnable, incorruptible, indelible, indestructible,
   ineffaceable, ineradicable, inexpugnable, invincible, invulnerable,
   irrefragable, irrepressible, nonperishable, quenchless, undampable,
   undestroyable, undying, unquenchable