The Collaborative International Dictionary of English v.0.48:

Importunity \Im`por*tu"ni*ty\, n.; pl. Importunities. [L.
   importunitas unsuitableness, rudeness: cf. F.
   importunit['e].]
   The quality of being importunate; pressing or pertinacious
   solicitation; urgent request; incessant or frequent
   application; troublesome pertinacity.
   [1913 Webster]

         O'ercome with importunity and tears.     --Milton.
   [1913 Webster]

WordNet (r) 3.0 (2006):

importunity
    n 1: insistent solicitation and entreaty; "his importunity left
         me no alternative but to agree" [syn: importunity,
         urgency, urging]