Hi Philip, it looks like maybe some of the existing edges that are right overlapping in the same area you are trying to cut may be making the intersection somewhat unclear.
Booleans and cutting operations can sometimes have difficulty if there is geometry that kind of slightly weaves in and out of the cutting surface.
It looks like doing a boolean with a line drawn off to the side divides faces where it should but does not end up cutting the object in half, but it should be possible to fix it by using Edit > Separate to break the faces of the two halves apart manually, I'll see if I can do that and post a result for you.
- Michael
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