It could be that when you mix your ingredients for pumpkin pie, you do so either too vigorously or too quickly. That causes unstable air bubbles to form: when you bake the pie it puffs up and as it cools and the air bubbles collapse, the pie caves in or splits.
When you take the pie out of the oven, immediately run a knife along the edge of the crust to prevent it from sticking to the sides and "pulling" the filling as it cools. Also, be sure you don't bake the pie too long: as it dries out, it can crack.
For more tips, watch our video, How To Make Classic Pumpkin Pie.
Recipe: Classic Pumpkin Pie