Why does my loop subdivide not extend around the whole shape? I am createing a model which has a cylinder shape extruded inwards, and wanted to create some sharper edges around it. I tried using the loop subdivide tool (Ctrl + R) but the "loop" part of it is only reaching half-way along the inner edge



The top portion of this is divided into thirds for this, and I'm not sure why this is happening.

These appear to be 4 sided shapes, so I don't think it's an ngon problem.
You probably have duplicated vertices. Here I ripped a few vertices (and moved them away which isn't the case in your model) to interrupt the flow of the loop cut:



This can be easily fixed by Remove Doubles.