My SD did it when she was 6. Since I was her stepmom (and had to care for her by myself sometimes) I wasn't allowed to do much in the way of punishment. I do know that when my SD would pester her mom, eventually her mom would give in just to shut her up so there was the payoff.
It got to be where she was rude to others as well. If someone offered to get her something, she'd always ask for two, then when told no, she would pout. At a friend's house she was offered water, and then she said "No, I want juice." When the mom said "well, we're drinking water now" my SD replied "I KNOW you have juice, I SAW IT in your fridge!" I was mortified and had to immediately pull her into the next room--where she sulked because she could not have juice (and then we left the playdate).
When left unhandled, this can escalate into being rude to others. She went for a few years with barely any playdates because no one wanted her over because she was so demanding and annoying.
She can also be spirited, fun and energetic!
How we handled it at OUR house (and at her mom's house she continued to pester and still does to this day now that she's 12 but does NOT at our house) is we told her that no means no, and if we have to say it again, no means never.
If we offered to buy her a small toy at the fair to be nice, if she asked for two she would not receive anything.
If she asked to watch TV and we said "no" and she asked again, then there would be no TV for 2 days (it was 2 days when she was younger, and 2 days is an ETERNITY for them!)
If she asked for dessert, and we said "no" and she asked again, then it would be no dessert for 2 days.
It took a few weeks of us enforcing this, and then it stuck. It took longer, I think, because she'd go back to her mom's where pestering got her whatever she wanted.
She no longer pesters. Sometimes if we say "no" then she might ask "well, when is a good time?" and that's a fine question to ask and is not pestering.
You and your husband need to pick a discipline for asking more than once and stick to it. If you don't she's going to pester other people in her life just like she does for you--and that's going to be a recipe for disaster!