The Court can order any case re-argued after a new Justice is confirmed, this happened with a couple of cases that were argued after Scalia's death. See, e.g.,http://www.scotusblog.com/case-files/cases/jennings-v-rodriguez/. They are most likely to do that in cases that were deadlocked 4-4, but we don't ever know for sure if that's the reason. Generally, though, if they have a clear majority (5-3, 6-2, etc.), they just decide the case.
