For me, whenever I read the bible, in regards to broken relationships, what I see in scripture is that we are to seek forgiveness and reconciliation quickly, (before we give our next offering). However we cannot make others reconcile..they must also want it. But when they dont, the usual advice, from Christians and non christians alike is to let it go and let them go if I love them. However, no scripture is referenced for this, and therefore it seems that by letting go I am appeasing the teachings of man rather than obeying christ.
Furthermore, if something is valuable, you would never actually let it go. If your house was marred by a flood...you would repair it. If your wedding ring dropped in the drain, you would go find it. If your child disappears, you would look for them. If someone asked you for your prized autograph baseball, you would not just simply let it go...you might sell it, perhaps, but it when adequate value has been met.
Why then, do we not give people the same value when God says to love them? Why do we not value relationship like we do a ring, or a home? If we did, surely this would attract people to Christ. Wouldnt trying to hold on, instead letting go, prove that someone is valuable?
So I'll start off with a couple of quick stories, and then give an answer to you.
About a decade ago, I heard the story of a man who went into ministry, I believe in south east Asia. He was a missionary for over 5 years. His daughter called him, and he told her that he needed to minister to people there, and would call her back later. Two days later, he got message that his daughter committed suicide. Later his wife divorced him. He spent the rest of his life a shattered man, that rarely left his house.
Another man, a pastor, got married to a woman. For whatever reason the mans parents did not like this woman. They did not approve of her, and had no interest in her. When they called, they would ask for him, and ignore his wife. When they visited, they ignored her, and talked only to him. One day he showed up with only his wife, and no kids. He sat her down in front of them, and explained this this was his wife, and that she was more important to him, than anyone else in the world. He gave them an ultimatum: Either treat her with the dignity and respect she deserves as his wife, or be cut out of the family. No holidays. No grand kids. They change phone numbers, and move to a new home. They will never see any of them ever again.
While the first story was tragic, the other the parents accepted his wife, and the problem was resolved. But he said that even to this day, if they had continued to reject her, he would have cut his parents out of his life, entirely and forever.
So what is my point?
Your main point is essentially right. We should struggle after the lost sheep, just like Jesus did. G-d would chase us to the ends of the universe, and he is able to do this, because he is G-d.
And we should struggle toward that end. And we should fight for our relationships when we can.
However, we must not be arrogant about who we are. We are not G-d. We are not Jesus. We are human beings, and we are limited. We can't do what Jesus did, because he is infinite, and we are finite.
And by the way.... about that.... you remember all those times in the Bible where Jesus went off to a far place alone? Where he was walking out on the water by himself, alone? On top of a mountain alone?
Why do you think Jesus needed space to be alone? He was G-d. He was literally the infinite creator. Why did he need time alone?
Forgive this non-pastor for putting my opinion on this....
I don't think Jesus really really needed time alone. I don't think he did that for himself. I think he did that for us, to be a model to us for how we should live.
How does that apply to your question?
Sometimes we need to let stuff go. Sometimes we need to admit to ourselves, we did our best, and now we have to let it go.
That missionary needed to let go of those relationships. He need to let go of those lost people, and go be a father to his family, and a husband to his wife. He needed to let it go.
That pastor, needed to let go of his parents, if they didn't stop harming his family.
I'm a person that has had a few specific relationships, that I cared very deeply over. And that relationship was so toxic and damaging, I finally realized I had to let it go. Doing that caused deep pain to me, but now I see it really was for the best.
I still care about them. I still want to see they are good, and doing well. But I can't have that relationship.
Fight for your relationships when you can. But understand some relationships are literally toxic, and you will destroy yourself, before you ever save them.
I was telling a friend this years ago... if your boat is sinking.... then you can't save someone by tie a rope around them connected to your sinking ship.
If you have a relationship that is drowning you, you are not going save them, you are just going to sink with them. Fight for who you can fight for. Stand up for whoever you stand for. Protect everyone that you can protect.
But you are not G-d. You are not infinite. You have limitations, and you need to protect yourself, or you won't be able to protect anyone.