"Always perseveres" is the last quality of love. (We could discuss "never fails," which I have not planned to. And we could discuss the possibility that the last four qualities form some sort of unit.) One might be tempted to put this quality in the same bucket with "patient" and "not provoked." I think those two deal with relationships and this one deals with circumstances.
Walking with someone through some type of trouble is different than walking through you own troubles, or walking through circumstances where another person has developed some type of animosity towards you.
There is a quote about Mother Theresa. Many people have gone into the slum of Calcutta to help people there. But, after a while, they went home. Mother Theresa went into the slums ... and stayed.
Just like God doesn't give up on us, but stays the course until the end, we need to stay the course.
I don't think this always means getting involved with something or someone, and never moving onto something new. But there is a tendency among many people to move on when the next glittery thing appears, or problems reach a certain threshhold.
It is staying until things work out, or improve, or until the parameters indicate one's part in the job is done, that shows love. Jesus had a purpose. It was to accomplish particular things. He did not need to walk for a long time, in terms of years. But he did have to walk along a very difficult road. And he stayed on that road until the end.