one thing you might want to check, is your tolerance for your split tool, maybe its attribute put up too high and that blocks you from clicking another point...so try lowering it down.

if not, most of time, your geometry isn't correct. You have an extra face, or edge. or vertex. or that polygon face you try to use the split too on isn't a flat face.

another thing you can try doing is just create one line at a time?...
maybe spliting too many lines, meses maya up?..