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The Collaborative International Dictionary
Importunateness

Importunate \Im*por"tu*nate\ ([i^]m*p[^o]r"t[-u]*n[asl]t), a.

  1. Troublesomely urgent; unreasonably solicitous; overpressing in request or demand; urgent; teasing; as, an importunate petitioner, curiosity.
    --Whewell.

  2. Hard to be borne; unendurable. [R.]
    --Donne. -- Im*por"tu*nate*ly, adv. -- Im*por"tu*nate*ness, n.

Wiktionary
importunateness

n. Quality of being importunate.