The Collaborative International Dictionary of English v.0.48:

Insupportable \In`sup*port"a*ble\, a. [L. insupportabilis: cf.
   F. insupportable. See In- not, and Support.]
   Incapable of being supported or borne; unendurable;
   insufferable; intolerable; as, insupportable burdens;
   insupportable pain. -- In`sup*port"a*ble*ness, n. --
   In`sup*port"a*bly, adv.
   [1913 Webster]

WordNet (r) 3.0 (2006):

insupportable
    adj 1: incapable of being justified or explained [syn:
           indefensible, insupportable, unjustifiable,
           unwarrantable, unwarranted]