What causes yogurt in sauces to split? How to prevent it?
Yogurt is a mesh of denatured milk protein that traps the whey.

When yogurt is over-heated those proteins tighten and squeeze out the extra whey. When the protein matrix is cut it will also leak whey.

To combat this add a little starch. A little cornstarch mixed into the yogurt will prevent the yogurt proteins from over-coagulating. All heated yogurt sauces that I have seen include starch for this reason.

I should also add that this problem occurs mostly with lowfat yogurt. Extra milk fat in yogurt will interfere with the protein's ability to coagulate the same way the starch does.