I know your question is why the quantum leap in increasing CPU... but just logically speaking, at some point, your OS and your DAW will start FIGHTING for resources, which then adds overhead to the CPU to manage this war, which might be causing the QUANTUM leap.
I am using an APOLLO (original old silver face) and can run in 192kz/24 bit, albeit I have to turn up the latency buffers on the Apollo/SPLAT to do this. Which isn't an issue, since I can monitor the input tracks in real time and then it doesn't matter for mixing (except I notice a lag when I push the sliders and buttons).
I am totally guessing on what is causing the Quantum Leap....
PS - I also had a similar problem a few years ago, and using the same theory, fixed my DAW by turning down the number of threads that SPLAT would use (to be one less that my CPU had) so that the OS wasn't contending for CPU cycles but I think that the bakers have put in some fix for this since then.