I should clarify that I can get over personal, unresolved conflicts as long as I no longer have to deal with that person much. If it's just a dislike on both sides, then I can ignore it pretty easily. It may bother me at first if I feel a a sense of injustice, but I will calm down quickly. Maybe if I run into them I will feel some discomfort, but otherwise, I cannot control everything, and so I put it out of mind.
However, there are some conflicts that cannot be avoided and must be dealt with head on. Let's say you're going through a divorce (which I am not, haha), then you have to resolve certain things legally. It must be taken care of. During that time when things have yet to be resolved, I can only imagine the anxiety.
I'm in the process of closing some matters and it's a massive headache. I know I will not resolve the personal conflict, and I don't care, but it's just getting to the point where I don't have to deal with this person anymore.