Why does the autopilot disengage even when it does not receive pilot input? After having read the disturbing

https://en.wikipedia.org/wiki/1999_South_Dakota_Learjet_crash

I'm left with the question as to why the computer allows for the autopilot to be disengaged when there is no pilot input.

Why doesn't it engage the stick shaker and alarm as normal, but maintain control until pilot input is received, or require the pilot to manually disengage the autopilot?

I'm not a pilot, so I'm sure there is good reasoning behind this. However, from my own naive perspective this is why it seems foolish to automatically disengage the autopilot:

This is what happened after the autopilot was disengaged:

"The target is descending and he is doing multiple aileron rolls, looks like he's out of control...in a severe descent, request an emergency descent to follow target."

Imagine that the crew did regain consciousness, they would find themselves in a disorienting situation, with an aircraft possibly damaged from aerodynamic stress when approaching mach 1 in an uncontrolled nose dive. This, compared to the autopilot simply maintaining attitude as best it can.

Until finally, this: "the aircraft hitting the ground at a nearly supersonic speed and an extreme angle."

The alternative being, with no pilot input that the aircraft would have maintained a somewhat stable attitude, deploys its landing gear, flaps, and prayed for the best -- that there just happens to be a fairly smooth piece of land, with no major obstacles in the way?

Now, I'm aware that all six on board were dead before the plane crashed. That doesn't mean there are no situations where a controlled crash landing is not preferable to an uncontrolled crash.

I'm not an avionics software engineer, so forgive me if I don't appreciate the complexity of the task -- but as a software engineer and someone with an IT education it seems to me almost trivial to extend the functionality for the aircraft to accommodate for this scenario with a mostly hard-coded procedure---yes, blindly landing at whatever is there and hoping (and with the system being extended with visual processing, perhaps, in the future). While I'm not even going to sketch a full proposal for such an extension here, it is part of my motivation for asking this question in the first place, so I'm simply mentioning it as that.

I can also mention, although I'm sure anyone qualified to answer this question will know about this case (and know it far better than I do), the Cornfield Bomber https://en.wikipedia.org/wiki/Cornfield_Bomber so if this is possible without any help from the computer, surely it would be possible with help, even from a computer that only has basic instruments (altitude, attitude, etc.) and no vision, yet simply attempts it "blindly" as far as visual processing is concerned.

Please keep in mind that I'm under no illusion that the plane will land without a scratch. This is a game of statistics, such as all safety procedures, and it seems (naively, I'm sure) that this might increase the chances of survival by some (probably slim) margin.

My own attempt at an answer:

I can only imagine that the reason such functionality doesn't exist, is because it is so rarely useful and considered too much of a curiosity. However, other crashes that also appear to be highly unlikely in general, have seen changes enforced in the aviation industry. So this isn't really a good answer.

The only other thing I can think of, is the omnipresent fear of AI. The idea to implement some AI, that could potentially, when given full authority of the plane, glide it into a building unintentionally, is just unthinkable for obvious reasons. While I sympathize with this view, I don't see why this is more likely than it happening with a plane flying without such a simple AI---both the AI and the completely uncontrolled plane would be flying just as blindly, both at risk of hurting innocent bystanders. The only difference is that the AI assisted plane flying autonomously (despite mostly blindfolded) does have a marginally higher chance of allowing for some survivors.
The "autopilot" is a fairly basic control system. Usually it is composed of just a few components (logically speaking) like a wing-leveler, heading mode, and altitude mode. The autopilot can control the aircraft usually through servo's connected to the control cables or through the hydraulics. External systems can feed into this to do things like follow a descent path, follow GPS/VOR routes, etc. The autopilot itself is basic.

The autopilot is designed to fly an aircraft that does not otherwise have any other issues. The autopilot is not designed to fly outside of normal operating circumstances. This means that when some kind of abnormality is detected (usually through the autopilot hitting its programmed limits) it will automatically disconnect.

In the Learjet case you cited, the autopilot continued to maintain altitude after the engines failed, but because maintaining altitude without engines means your speed will decrease, the autopilot disconnected before the aircraft stalled rather than fighting the pilot through a stall. It assumes that it is safer to automatically hand-off than require the pilot who is now trying to stabilize the aircraft to also have to worry about disconnecting the autopilot.

Most autopilots give some kind of warning that they've disconnected. This can be things like a chime, voice alert, stick shaker, etc. It's the autopilots way of saying "I've reached the limits of what I can control, you need to take over now". Otherwise it could potentially make a situation much worse.

The cornfield bomber was not on autopilot when it crashed. It just regained stability as a result of the ejection and remained on a fairly level (but descending) path until it bellied into a field (and continued to run/move for quite some time).