I say forget about persistence for now. Are your intentions honest? Cos dishonest intentions can lead to some fucked up things. Even if you're a good conversationalist, friendly and interesting, if there's no sexual attraction in the interaction you're gonna run into problems. Make it clear from the get go that you're excited by and like this girl. Create that spark.
Everything else comes from that. This ''echoing'' you mention could be a sign that the girl thinks ''wow, we're friends and he's nice, but he keeps messaging me so he might want something more from me... but i can't call him out on it because he hasn't said anything to prove it... i'll try not make it awkward so i'll just play along.'' As you can see, everyone loses: you end up frustrated and she gets stressed.
Try not to be approval seeking. Do things for you, get what you want, and get it in style. Let her know that you're into her. She'll most probably like that, even if she might not admit it out loud at first.
...and that's where the persistence comes in.
