Do girls like persistence?

I like this girl who I've known for years, and I know she likes me because when I put statuses about personnel things she asks me whether I want to talk about it, so clearly she does like me as a friend.

I keep asking whether she wants to hang out, and she says she would love to, but when I message her on messenger she never sees the messages and can sometimes end the conversation too soon.

Should I continue to try and get to know her better?