The Collaborative International Dictionary of English v.0.48:

Importunate \Im*por"tu*nate\ ([i^]m*p[^o]r"t[-u]*n[asl]t), a.
   [See Importune.]
   1. Troublesomely urgent; unreasonably solicitous;
      overpressing in request or demand; urgent; teasing; as, an
      importunate petitioner, curiosity. --Whewell.
      [1913 Webster]

   2. Hard to be borne; unendurable. [R.] --Donne. --
      Im*por"tu*nate*ly, adv. -- Im*por"tu*nate*ness, n.
      [1913 Webster]

WordNet (r) 3.0 (2006):

importunately
    adv 1: in a beseeching manner; "`You must help me,' she said
           imploringly" [syn: beseechingly, importunately,
           imploringly, pleadingly, entreatingly]