Dating an Emotionally Unavailable person

Hi everyone. I'm Mike

I am a new member of this community.

I am in a 7-month relationship with a young lady that I would deem a superb young lady. She is always there for me, as I am for her. She tells me she loves me, and in many small ways, she always shows it. I am her first relationship, even though we are adults, and she is unsure how to be the perfect girlfriend. I assured her that it's ok and that I am patient while she adjusts herself to being in a relationship. She is an amazing girlfriend, except for one factor that is important to me. She is emotionally unavailable.

She lost her mother a few years back and since then, she has this view that everyone who comes into her life will definitely leave her at some point in life. This is my problem because everytime I get close to her or she feels hersefl getting to close, she shuts me out and pushes me back and it frustrates me. I have told her countless times that I am here to stay with her through the good times and bad times and she always tells me that she believes that God wants us to be together and eventually get married. 

If so then why push me away? I see at times she tries to do little things to reassure me that she loves me but now recently whenever we have vulnerable conversations, she would not respond to my messages, even though she is online and comes about like she is outright ignoring me and I don't knwo what to do becaus eI plan to marry her after I graduate from med school in the next few years

 Do you have any advice? I do love her, and I don't want to have to leave her.