This is a z-order issue between the splitter and the statusstrip. When you have a control you want to dock fill and one or more controls you want to dock top, left, right, or bottom, you have to have the fill control be the first in the z-order.
The better way is to open the Document Outline tool, select the SplitContainer and use the up or down buttons to change its z-order.
I should add that in Winforms the z-order is specified by the order in which you add controls to the Controls collection. That order determines the order the associated system controls are created, hence their z-order. Using the Document Outline tool to alter z-order simply causes the generated code to be re-ordered.