how long do you give a friend who’s mad at you before just having to give up ?

so one day i realized that my best friend and i were no longer talking the way we used to. i knew i wasn’t always the best friend so i sent a message asking to know what i did wrong, apologizing, and asking to go back to normal. he claimed he didn’t care to hold grudges and agreed to go back to normal. after a few days of me trying and trying to initiate conversations and it feeling like he didn’t feel like talking to me, i thought maybe i was forcing it so i stopped and waited for him to come naturally to me but it never happened. that was over a month ago.

we didn’t talk to each other much since then but then 2 weeks ago i sent another message, trying to ask what i did wrong/what was frustrating him to the point where he no longer felt like talking to me. he again told me nothing when i was trying to have a conversation about what i was doing that was wrong and just told me he needed more time to become close again. so i spent the past 2 weeks checking up on him, trying to talk to him abt things he liked, etc. i sent another message to him a couple days ago asking him how he felt about the friendship now and he said he needs a little more time to be close friends again. this is the start of the 3rd week of me talking to him first every single conversation we have, trying to talk to him/check up on him and i don’t know how much longer im supposed to do this. i don’t want to give up on this friendship because we genuinely felt like best friends at one point. but i tried over a month ago and i’m trying again now for 2 weeks straight and he still isn’t ready to be close friends. at what point do i just stop because it’s not healthy for me to keep doing this?