Need some advice regarding a breakup and how to act now

So basically there is this girl who I dated for a while and things in her life got to a point where she simply didn't have time to spend in our relationship so I broke up with her. I still had feelings for her but she simply didn't have the time to commit to a relationship. After a few days of us talking a lot about the breakup and the reasons we kind of reached an agreement where after a few weeks when her schedule would be less hectic we could try to start spending time together again.

During those few weeks things were pretty good, we went on a few dates as friends and talked everyday till we went to bed. Suddenly one day she never answered my messages and I grew worried because she always responded. I sent 4-5 texts over the course of 48 hours without getting a response from her and when she finally did respond she flipped out at me and really said some harsh things. Things from that point were really rough between us, she ended up apologizing to me after we didn't speak to each other for a couple weeks(we work together BTW). After the apology I thought through what I was feeling and I told her I still had feelings for her but I knew that a relationship was out of the question for now. I told her I needed some time to kind of stay away and clear my head.

I spent about a month away from her and at the end of the time I decided that I valued her friendship and though I did not want to date, I wanted to try and be friends with her. So three weeks ago I started slow with simple hi’s and bye’s and we started joking around at work and I messaged her outside of work to just casual conversation. I never suggested hanging out or anything of that nature. The issue I’m having is that while I am trying to initiate conversation and build the foundations of a friendship, she is either very receptive or very defensive and negative towards me. And it seems to switch in the matter of an instant. I helped her arrange a meeting with our boss and she ended up getting a raise after telling me she was very nervous about speaking with him. Then later that day she walked right by me and clearly ignored me and didn't look at me or even say hello. It hurt my feelings that she did this after I went out of my way for her regarding her getting a raise. I told her how I felt and after being very defensive with me she ended up apologizing and was very much her old self with me the rest of the night. The next day she acted oddly around me all day. When I saw she was getting ready to leave I told her to have a nice weekend and I got a very fake smile in return. I asked her if she was OK and she said yea without looking at me. I told her she seemed to be acting a little weird around me today and she looked at me, gave me a weird smile and said she had to go and literally ran past me and out the door. I asked her later what that was all about and she once again got very defensive and attacked me. She says not everything has to do with me and she does not owe me anything, especially an explanation. My response to this was that I agreed that her personal life is her own and what I wanted was simply to work on a friendship. I told her I hoped whatever it was that was bothering her got better and I am there if she wants to talk about it sometime.

So after my long background story my question is what is going on with her? Should I continue down this path or just forget it? It is important to me that we become friends and I explained that to her. I asked her if she wanted to try and be friends and she said yes after evading my question initially. I am going to be giving her some space because she is clearly stressed. But what else can I do, if anything, to help her and our friendship?