The Collaborative International Dictionary of English v.0.48:

Inflexibility \In*flex"i*bil"i*ty\, n. [Cf. F.
   inflexibilit['e].]
   The quality or state of being inflexible, or not capable of
   being bent or changed; unyielding stiffness; inflexibleness;
   rigidity; firmness of will or purpose; unbending pertinacity;
   steadfastness; resoluteness; unchangeableness; obstinacy.
   [1913 Webster]

         The inflexibility of mechanism.          --A. Baxter.
   [1913 Webster]

         That grave inflexibility of soul.        --Churchill.
   [1913 Webster]

         The purity and inflexibility of their faith. --T.
                                                  Warton.
   [1913 Webster]

WordNet (r) 3.0 (2006):

inflexibility
    n 1: a lack of physical flexibility [syn: inflexibility,
         inflexibleness] [ant: flexibility, flexibleness]
    2: the quality of being rigid and rigorously severe [syn:
       inflexibility, rigidity, rigidness] [ant:
       flexibility, flexibleness]