Either it has some CPU/cache/memory hardware problem that is causing page table references or some critical bit of the kernel got corrupted on the CF card - "page fault while in kernel mode" should never "just start happening".
The easiest thing to do is to take out the CF card and re-write it a new good pfSense nanoBSD image. If that works then you are in luck. If the CF card gives errors when writing it, then you know to get another CF card.
If you still get "page fault while in kernel mode" on a clean pfSense boot, then there has to be some hardware problem on the board. Since the CPU, memory is all fixed to the Alix board there is not much benefit in knowing if it is CPU or memory or…