You know those people, who are so focused on what they want, that even when it is reasonable, their asking for it over and over gets really annoying? They, and their questions, can be called importunate.

Importunate rhymes with "unfortunate" and importunate questions, in their annoying persistence, are unfortunate indeed. You'll see in importunate the Latin root port, which means "harbor." An opportune wind helps you get into port safely; an importune one, unfortunately, doesn't.

Definitions of importunate

adj expressing earnest entreaty

“an importunate job applicant”
beseeching, imploring, pleading