importunate \im-POR-chuh-nit\, adjective:
Troublesomely urgent; overly persistent in request or demand; unreasonably solicitous.

An emperor penguin in captivity starved to death by feeding all his rations -- about six pounds of fish daily -- to an importunate chick.
--Jeffrey Moussaieff Masson, The Emperor's Embrace

The play is a cacophony of importunate ringing doorbells and telephones, of pleas both professional and romantic from an exasperating assortment of colleagues and admirers.
--Ben Brantley, "Present Laughter," New York Times, November 19, 1996

Jokes form a kind of currency, such that a wise-crack from the most importunate beggar may bring instant reward.
--Max Rodenbeck, Cairo: The City Victorious

Importunate is derived from Latin importunus, "unsuitable, troublesome, (of character) assertive, insolent, inconsiderate."