Should I give up on the relationship?

Me and my boyfriend of 9 months keep arguing over immature actions like giving the silent treatment when one does something that upsets the other. It leads us to break up on several occasions. We tell each other to change buy we can't seem to do that. I love him very much. I care about him and my family has gotten used to him. This is the first time I have fallen in love with someone and I don't even know if it's worth it. Because he gives up easily. He doesn't do anything to try and win me back. He just says okay and goodbye. I always end up texting him again and trying to make it work. It's hard to let go. And I am so conflicted.