insistent
Not giving up and firmly repeating a demand or belief.
When someone is insistent, they refuse to give up on what they're asking for or what they believe. An insistent person keeps pushing their point, repeating their request, or standing firm on their position even when others resist or ignore them.
Picture a younger sibling who wants to play with you: “Can we play? Please? Come on, just one game? Please?” That's insistence. Or imagine you're certain you saw a meteor last night, but your friend thinks it was just an airplane. If you keep explaining what you saw, bringing up details, maybe even looking up meteor showers online to prove your case, you're being insistent.
The word can carry different feelings depending on the situation. Sometimes insistence shows admirable determination, like a scientist who insists on checking her results one more time before publishing, or a student who insists on understanding a concept rather than just memorizing it. Other times, it can feel pushy or annoying, like a telemarketer who won't accept “no, thank you.”
Notice that insistent people don't just ask once and give up. They persist, they repeat, they push back against resistance. You might describe someone's insistent knocking at the door, or the insistent beeping of an alarm clock that won't let you sleep in. When something or someone is insistent, it demands attention and won't be easily ignored.