The Collaborative International Dictionary of English v.0.48:

Unsupportable \Un`sup*port"a*ble\, a.
   Insupportable; unendurable. -- Un`sup*port"a*ble*ness, n.
   --Bp. Wilkins. -- Un`sup*port"a*bly, adv.
   [1913 Webster]

WordNet (r) 3.0 (2006):

unsupportable
    adj 1: not able to be supported or defended

Moby Thesaurus II by Grady Ward, 1.0:

28 Moby Thesaurus words for "unsupportable":
   baseless, controvertible, empty, groundless, idle, ill-founded,
   insupportable, intolerable, unattestable, unbased, unbearable,
   unconfirmable, undemonstrable, undemonstratable, unendurable,
   unfounded, ungrounded, unprovable, unsubstantiatable, unsupported,
   unsustainable, unsustained, untenable, unverifiable, unwarranted,
   vain, without basis, without foundation