it may have reached max elevator to maintain the attitude for the speed at that height
This can be a problem with older autopilot types, even the NG aircraft have a rather basic autopilot, carried essentially over from the earlier models, with minor improvements...at least according to a good friend of mine who was an instructor on the NG series.
In fact, I asked him specifically about this.
Also, he mentioned that there was just one aircraft that he had flown (and is now back flying) which had the very best autoflight system he had come across, one that does not trip either off nor to CWS in the event that the elevator runs out of authority (all-flying stab, elevator mechanically connected thereto), so these aforementioned nuisance trip problems simply do not occur....out of trim annunciated for the pilots, yes, well in advance.
The design is over thirty five years old, and still works faithfully.
TriStar.