the knife tool (err line cut) can be very fickle. I've noticed it doesn't do the cuts I'm asking for and I've had to use the Polygon Pen tool instead. In your case you may want to try a couple things. I tend to hit space bar after I've laid down my cut for it to apply it. I also tend to not use the Snap tools (which I hate anyways in C4D compared to other tools) while using the knife tool. You can create angled cuts at 45 or 90 degrees by holding down the SHIFT key before starting to use the knife tool on your mesh.
Lastly, make sure you look at the options when using the Knife tool to give you more ability to tweak your cuts as you do them. The one I toggle mostly in the attributes is the Visible Only because sometimes I want to slice right through a model, even on the other side. The other interesting one is "Preserve N-Gon Curvature" which may be useful for you when cutting a rounded object.
Also, I have to remind myself Maxon decided to call it "Line Cut" versus "Knife". 😛