A divorce occurs when a Mii longer wants to be sweethearts/spouses. In order to find out a Mii wants a divorce, go to a Mii that has a emotion/orange problem, then tap the bubble. Then they will say "Things aren't going so great for me and [Mii Name].
A divorce can be resolved or a fail, depending on a Mii's relationship in the Compability Tester machine.
If a Mii has a divorce, they can be back together, but it will take some time.