The Collaborative International Dictionary of English v.0.48:

Insolubility \In*sol`u*bil"i*ty\, n. [L. insolubilitas: cf. F.
   insolubilit['e].]
   [1913 Webster]
   1. The quality or state of being insoluble or not
      dissolvable, as in a fluid.
      [1913 Webster]

   2. The quality of being inexplicable or insolvable.
      [1913 Webster]

WordNet (r) 3.0 (2006):

insolubility
    n 1: the property (of a problem or difficulty) that makes it
         impossible to solve [syn: unsolvability, insolubility]
         [ant: solubility, solvability]
    2: the quality of being insoluble and difficult to dissolve in
       liquid [ant: solubility]