importune
To keep asking for something in an annoying, pushy way.
To importune means to ask someone for something repeatedly and annoyingly, refusing to take no for an answer. When you importune your parents to let you stay up late, you keep asking over and over, wearing them down with constant requests until they give in just to make it stop.
The word carries a sense of being pushy or overly persistent. A younger sibling might importune you to play with them when you're trying to read. A street vendor might importune tourists to buy souvenirs, following them down the block despite their polite refusals.
Importuning is different from simple persuasion or making a good case for something. When you persuade someone, you give them good reasons to say yes. When you importune them, you're just being relentless, hoping they'll give in just to make it stop. Think of it as the verbal equivalent of poking someone over and over.