Networking without feeling pushy - any advice?

I sent 9 messages on a professional network and got two replies. I have read a lot of threads here and could not find my exact situation. Some people reply with short answers. Did any turn into leads?

Follow up with a thank-you and a short update. One of my chats led to a referral a month later.

Thanks for writing this out. I went through something close to it 2 months ago, and it got easier once I kept a simple log of every call and form.