Some times when a dispute has gone on for a long time it gets stuck even long after it has been resolved. Even if it turns out to not have been important. It can sit in memory and colour every action even those that are not related. Even unrelated things can bring it up again. When this happens there is really nothing to do but separate on as friendly a base as possible. Some times this is all it takes to break the cycle and they can stay friends. The odd time they will get back together but this takes a lot of work on both parts. Sometimes it is worth it. It takes letting go of the past in the form of accepting that the original dispute is not relevant to the present. Not forgot though, just used as a lesson. It can be hard if this is not the first relationship this dispute has shown up in. Remember core beliefs? Throw one or two of those in and you have a recipe for disaster.
So all the help in the world is no help if you keep going back openly to the original dispute. People have pride remember.
It doesn't help too if one person is trying to make amends and the other won't accept it. Whether to get their way or just because they feel like it. Sometimes this is unintentional. Up bringing or core beliefs again? Who knows.
Sometimes a cooling off period in the form of a separation is necessary. You know the saying,"If you love someone let them go, if they don't come back they were never yours". Not totally true. There can be reasons to get together that are not there after a time. And people can change.
So if you do have to separate, stay friends so it doesn't colour your future, last thing you need is another negative core belief messing you up.
I think a lot of this is relevant to work also. Probably more so in fact. After all there is less to lose.
Ashley, I agree with your first paragraph but both parties have to be willing to or capable of accepting compromise. Sometime one party is not capable of doing the compromise for physical or mental reasons. Age can also interfere. I believe two people have to really want something to work, for it to do that.
Just my opinion. Just my experience.