When using split poly tool you have to start and end on existing edges. If you try and draw in the the middle of the face you might get one line but will usally disapear when you hit enter.

What I usally do is draw a few more edge lines going vertically and horizontally in the area that way it gives you more edges to use split poly tool to cut out the shape you are trying to get.

Its a bit hard to write in words hope you understand.