The Collaborative International Dictionary of English v.0.48:

Irredeemable \Ir`re*deem"a*ble\, a.
   Not redeemable; that can not be redeemed; not payable in gold
   or silver, as a bond; -- used especially of such government
   notes, issued as currency, as are not convertible into coin
   at the pleasure of the holder. -- Ir`re*deem"a*ble*ness,
   adv.
   [1913 Webster]

WordNet (r) 3.0 (2006):

irredeemable
    adj 1: insusceptible of reform; "vicious irreclaimable boys";
           "irredeemable sinners" [syn: irreclaimable,
           irredeemable, unredeemable, unreformable]
    2: (of paper money) not convertible into coin at the pleasure of
       the holder

Moby Thesaurus II by Grady Ward, 1.0:

33 Moby Thesaurus words for "irredeemable":
   beyond recall, beyond remedy, cureless, gone, graceless,
   immedicable, inconvertible, incorrigible, incurable, inoperable,
   irreclaimable, irrecoverable, irreformable, irremediable,
   irreparable, irretrievable, irreversible, irrevocable, lost,
   past hope, past praying for, remediless, ruined, shriftless,
   terminal, undone, unmitigable, unpayable, unredeemable,
   unregenerate, unrelievable, unsalvable, unsalvageable