My club just got a very nicely equipped Bonanza with a King KFC-200
A/P system installed (along with a CNX-80 GPS). I think I've got most
of it figured out, but yesterday something happend which I didn't
understand.

The active leg in the GPS was a course of about 230, with a stiff wind
from the south. I was about 2.5 miles right of course, and 30 miles
from the next waypoint. I put the course pointer on 230, the heading
bug on 190, and selected FD, HDG, ALT, and AP-ON, and watched the
cross-track error on the GPS; it was decreasing slowly, so I figured I
had a nice shallow intercept angle set up. I then hit the NAV
button. The NAV and ARM lights came on, as expected.

Eventually, Otto intercepted the desired course (as indicated by the
GPS XTE going to zero and the HSI course deviation bar centering.
What I expected to happen at this point was that the HDG and ARM
lights would go out and the CPLD light would come on, and Otto would
start tracking the course. Instead, it just stayed in heading mode
with ARM lit up, slowly taking us left of course. When I recycled the
NAV button, it instantly went into coupled mode and started tracking.

Is my understanding of how ARM/CPLD works in error? Is it possible
that the very shallow intercept angle I had set up (just a couple of
degrees) had somehow fooled the coupling trigger circuitry?