Why does the autopilot disengage even when it does not receive pilot input?
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).