When do you give up on someone? Advice please!

I know this is Kind of long, but I needed to create some sort of picture.

I met this guy online who lives 2 hrs away from me and we talked for 3 weeks before we had our first date where we met in the middle at a very nice Italian restaurant and everything went great. He kept telling me how beautiful I am and that he is sorry he keeps babbling because he is so nervous. Then right after our first date on my way home he sent me this song “wannabe” by Dylan Schneider telling me this how he thinks of me and everything. During that week we would tell me that he could fall in love with me in a week and really cute stuff like that. But I was really afraid of my feelings for him so fast, so I asked him if we were moving to fast and if we were crazy for having our feelings so strong so quick. The only reason I was afraid is because my last 2 relationships ended with me being cheated on and moved quickly in the beginning. I wanted things to be different. So he said that he agreed with me that maybe we should slow down and get to know each other and things which I’m fine with. So on our second date I went to his house and we had dinner and went in his jacuzzi and had fun were we declared we were dating exclusively but not the girlfriend boyfriend title. I stayed the night but we didn’t have sec or anything. On our third date I went back to his house and I cooked him and his dad dinner. Sitting in the living room with his dad, he was always holding my hand, touching my knee something to show affection and I have never had that before and it made me happy. So He started working for with his dad at in the oil industry and he warned me he was about to be extremely busy, but I told him I was a patient women and didn’t mind. So after our 3rd date I didn’t see him for a whole month but it was okay because he would always text me, and then we had our nightly phone calls.. But then one day I didn’t hear from him all day so I was worried, one day turned into two days, which turned to three days when I finally heard from him. I told him that I don’t mind if he doesn’t want to talk to me everyday, but a simple I’m okay or I’m alive text is fine. So then I didn’t hear from him again for another 3 days, so I sent him a long ass text explaining my feelings and what I wanted for us to work.. He never responded, so I thought he was done with me. 2 days after I sent the text I called him so I could just have closure or something which he finally called me back and just said he was busy and going through stuff with his family, so I automatically felt guilty and selfish for just wanting to talk to him or just get a response. So we worked things out the next two days I would just simply send him have good day at work texts, got no response, so I stopped. Called him four days later and no answer, hasn’t called me back. I know I should be done with him, at least that’s what my brain is telling me which would be smart because if he really wanted me he would take the 2 seconds for a simple text at least I think. But my heart is telling me that I’m being selfish that he is busy or some stupid thing like that. But in order for me to be done, I should break it off with him but I can’t break it off with him, if he won’t answer. How long do you give a person till you officially give up? Or am I already dumb for waiting this long? Is it cheating if I don’t officially break it off, and try to move on or move forward? Any advice would help please.