There is a bug here, but it's not what you might think😅
Your issue is most likely an issue with one of your axes (pitch, roll, or yaw) sending spurious signals to the sim and disconnecting the autopilot. After engaging AP1, any major movement of the joystick or rudder pedals turned off the autopilot straight away in my sim with the 3 chirps.
Now here is the bug: If i engage AP2, no flight control inputs are disconnecting the autopilot. Pitch and roll axes from my joystick do not seem to be registered by the aircraft by looking at the yoke/control column, or on the F/CTL page. Yaw axes input from my rudder pedals do indeed show the rudder pedals in the aircraft moving, but there is no yaw applied to the aircraft, and on the F/CTL page, the rudder remains neutral.
The simconnect AUTOPILOT_OFF command does disconnect AP1 or AP2 whichever is enabled. The AUTOPILOT_ON command always engages AP1.