I think it's more a personal problem than a general problem of etiquette.
My advice is to not do it, let this friend alone on that topic or on any other.
It does not matter who is right or who is wrong (or who is more wrong/right. Because it's likely not that clear cut).
What matters is that's it is going on for so long, too long, and both of you are suffering from the situation. Them because they most likely see your behaviour as annoying, if not as downright harrassment; you because you still hope for an improvement that likely won't happen.
The respectful thing to do is to let them alone. Again it does not matter who's more right or more wrong.
If you're more wrong then accepting their desire to be let alone mitigate whatever you did wrong. It's good for every party.
And if they are more wrong, it does not make it absurd to be the one doing the reasonnable thing. You're allowed to take the mature step in any case. Again, good for both.
I hope it does not sound too rude, that's not my intention, it's more that I'm worried that you're losing your time and energy to try to fix an unfixable situation.