The Collaborative International Dictionary of English v.0.48:

Infelicity \In`fe*lic"i*ty\, n.; pl. Infelicities. [L.
   infelicitas: cf. F. inf['e]licit['e]. See In- not, and
   Felicity.]
   [1913 Webster]
   1. The state or quality of being infelicitous; unhappiness;
      misery; wretchedness; misfortune; lack of suitableness or
      appropriateness. --I. Watts.
      [1913 Webster]

            Whatever is the ignorance and infelicity of the
            present state, we were made wise and happy.
                                                  --Glanvill.
      [1913 Webster]

   2. That (as an act, word, expression, etc.) which is
      infelicitous; as, infelicities of speech.
      [1913 Webster]