Is there hope or should I give up?

My ex and I broke up about 9 or 10 months but continued talking every day until 2 months ago when I told him I can’t keep talking to him. We were together for 2 years and broke up because we were both too immature to handle life issues and our communication took a bad turn. His mental health is also not great. After we broke up there was a lot of lying on his end and mistrust and a lot of arguments. It got to a point where I could not continue talking to him anymore. Since making that decision I have gone back on it multiple times. I’d contact him in highly emotional states and ask for us to talk a little again. He’d always shoot me down and say that while he misses me, he needs to focus on himself and is trying to move on from everything that happened. Every time I reached out it would end up in an argument as well. The last time I talked to him we argued and then both ended up apologizing for our actions. I’m trying to do no contact now and focus on myself. Should I try contacting him again after all this or is there no hope for us?