jmeg8237 I can jiggle the power plug connecting to the AAP, and feel it moving inside, and the power light on the AAP goes on and off with that movement.
The USB Type A connector and axial power connector without retaining screws (like the ones ZWO use in their cameras) were not meant for devices that moves. They were spec'ed for devices that sit on your desk or table. You might also find that the disconnects occur more often with sub freezing temperatures (albeit, you probably don't have that problem in Florida :-).
One thing that you can help reduce the problem is to strain relief the USB and the power cable.
At the point where the USB cable or power cable exits the camera, double the cable back onto the cylindrical body of the camera, forming a U turn in the cable. Then using either large cable ties (two in tandem if needed to get a long enough circumference), velcro straps, or Gaffer tape, tie the cable to the body tightly (using two sets of cable ties if needed) so that there is no movement. Tighten the cable strap when it is cold, just in case (or place the camera in your refrigerator beforehand).
Adding Gaffer tape right at the connector itself will help too.
Basically, try anything to prevent the connector from moving when you slew the mount. Especially watching for in-out movement of the connector too (hence the comment about Gaffer taping the connector body to the camera body).
The last resort (if you don't move the camera between different OTAs) is to use Siicone RTV like this instead of Gaffer tape:
You can still cut the gel like material to remove it, but I am sure ZWO would not warranty the camera :-). RTV has been used in spacecraft electronics to hold cable bundles in place since back in the 1960s and 1970s.
The worst is when you just have the cables dangling from the camera itself, that you see in cringe worthy pictures people post.
Higher end camera manufacturers use the kind of USB, DB-23 and power connectors with retaining screws.
Finally, double check that the power plug that you use is the 5.5mm/2.1mm kind and not the 5.5mm/2.5mm kind. Try plugging it (unpowered!) into a known 5.5mm/2.5mm socket and if it goes in, it is the wrong (2.5mm) plug to use.
There are too many cheap connectors around with poor springs to contact the male pin in the socket; I have even seen plugs from Amazon that have no springs). I recommend making your own cables using good connectors that you can buy from Mouser or DigiKey.