Boyfriend distant and cold after fight. How to approach the situation?

Anonymous
So me and my long distance boyfriend ( we do meet monthly tho ) had a fight 2 weeks ago.
From that time he is very cold. We talked it out, both apologized, but he is still so weird.
When we get in fight he always shuts down, shuts down intimacy, and minimize our communication. He said that we should talk less due to his busy days at work because talking and texting takes his energy.

I asked him if he thinks we should just let all go and end things since it’s so hard for him to get out of the bad vibe, he kept on saying no.

I don’t know how to approach him and how to give him space, without looking like I gave up on him. Help me please?
Boyfriend distant and cold after fight. How to approach the situation?
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