When does sibling rivalry typically go away?

Never. Siblings may compete their entire adult lives although it usually is no longer physical. Who is their parents' favorite, or who is the most successful are some of the areas that involve rivalry.
Varies with setting. Sibling rivalry is one of the natural stages of emotional growth in families. It clusters around school age as kids compete for their parents validation & provides a proving ground for acquiring skills of conflict resolution. Parents need to contain the process rather than stop it. Feelings go to & fro but the family unit should be supportive & allow them to run their course.