Okay. Where to start...
I have the Stream Deck XL and Stream Deck Plus. I am running MSFS 2020. I am using the PMGD 737-800. I downloaded the AAO Scripts and StreamDeck XL & PLUS from Guenseli (https://el.flightsim.to/file/32434/pmdg-737-aao-scripts-streamdeck-xl-profile-alpha) and followed install instructions on his page to the letter. The entire setup fired up and worked great for about ten days. Two days ago, mid flight I encountered this issues I am having for the first time.

THE ISSUE:
In flight, (and on the ground at least once, so it's not something to do with flight) the Stream Deck will freeze up completely. None of the buttons will respond (not even the image depress animation that you get when pressing a stream deck button). But that's not all... for some strange reason that I can't imagine how it happens, the aircraft autopilot will start to follow a random course in a random direction when the freeze happens. And twice, when this has happened, the aircraft has literally nosed strait up or strait down and the toke is visibly being "held" in a direction. I do not have any buttons or axis' mapped through AAO, I am only running the PMDG 737 buttons scripts and the "PMDG_737MSFS_Data" that was included in the above link. If I disconnect and close AAO and Stream Deck's software, I still do not have Autopilot control until I turn it off, cycle the FDs and AT and then reenable everything via mouse input. This hang/freeze can and has happened when I am not interacting with either the sim or the stream deck, so I am not directly triggering the event. The hang ups in sim DO NOT HAPPEN when I fly without using AAO/Stream Deck, so I am as sure as I can be that it has something to do with one or both of them.

THINGS I HAVE TRIED:
I have made sure Stream Deck is on my primary monitor. (that was a known issue regarding the stream deck itself)
I have verified that there are not any firewalls interacting with either Stream deck or AAO in any way
I have verified that the WebAPI port 9080 is open and reserved for AAO.

I have uninstalled and reinstalled:

-AAO (and all scripts from the link) by removing the application and everything related to it in %appdata% Local and Roaming
-Stream Deck by doing the same as above, removing all plugins and files related to the program

I have attempted to recreate the event but I haven't been able to reliably or predictably figure out the cause. I am not very sure how the scripting interacts with the sim or stream deck, but in my uneducated state, it seems that there might be some hang up in that interaction. But I have no way to know for sure (obviously).
I really enjoy using AAO and the stream deck together, but I am getting really frustrated with it and at this point, I would just like to know if there is a solution or if I need to give up and go back to using my mouse to click the cockpit items. 

It sounds like a binding issue , the same binding is bound on your stream deck and yoke or throttle and causing it to freeze. Unplug your yoke , throttle or controller see if the problem goes away. If it does you know its a binding on the stream deck and you can check the bindings on it to find what one is causing the conflict.

First: save yourself the trouble of uninstalling and reinstalling. That does nothing.

Question: Can you still change the StreamDeck profile when this happens (=in the Elgato software)?

In general, all these assets (StreamDeck plugin, AAO, the sim, PMDGs internal software) don't depend on each other, the communication is asynchronous. They don't care if one of them is there or not, and I can't see how they could compromise each other like this.

But. You are the second person reporting trouble with the PMDG autopilot while using AAO and having a Streamdeck present (not necessarily using the profiles though). But I also heard that people are having trouble with the PMDG AP regardless = without AAO or StreamDeck, but no details. The common denominator seems to be the StreamDeck software, but again, I don't see how that could be possible. The PMDG AP is (most likely) a part of their programmatic modules, and it seems highly unlikely that something could mess with it. It is obviously happening, but why or how, or what ingredients this needs to happen, is still unclear.

 

Are you running Windows 10, or Windows 11. Is your windows version 22H2?

1 hour ago, somiller said:

Are you running Windows 10, or Windows 11. Is your windows version 22H2?

You mean me? 
The test system is running Win 11, 22H2, build 22621.1105. But that is hardly a good comparison, there is A LOT of stuff on and attached to this computer. My MSFS on a whole is very unstable.

 

13 hours ago, Lorby_SI said:

First: save yourself the trouble of uninstalling and reinstalling. That does nothing.

Question: Can you still change the StreamDeck profile when this happens (=in the Elgato software)?

In general, all these assets (StreamDeck plugin, AAO, the sim, PMDGs internal software) don't depend on each other, the communication is asynchronous. They don't care if one of them is there or not, and I can't see how they could compromise each other like this.

But. You are the second person reporting trouble with the PMDG autopilot while using AAO and having a Streamdeck present (not necessarily using the profiles though). But I also heard that people are having trouble with the PMDG AP regardless = without AAO or StreamDeck, but no details. The common denominator seems to be the StreamDeck software, but again, I don't see how that could be possible. The PMDG AP is (most likely) a part of their programmatic modules, and it seems highly unlikely that something could mess with it. It is obviously happening, but why or how, or what ingredients this needs to happen, is still unclear.

 

Understood. Honestly, just habit of "turn it off and on again" thinking. 

Answer: Yes, I can go to the stream deck application and use the drop down to change the profiles to something else. However, the buttons still do not respond (it won't open another program or switch to a different profile using the buttons on the stream deck itself). This hand usually resolves itself after about 2 minutes or after terminating the application in Task Manager.

So, not dependent on each other. Understood. 
I have begun the reinstall of MSFS 2020 on a new M.2 SSD (I had been meaning to move it for a while, so this was a good excuse to start fresh.) and that will start me with a clean install of all control profiles, all addons like PMDG, and hopefully it is like jason74 suggested and it's a "binding" issue where I had some kind of multiple input problem. 

I am running Windows 10, current on all my updates and driver versions for all hardware. 

Would there be any log files anything that could help sort out what is going on? Would eliminating all keyboard keybinds maybe help? I don't use they keyboard except to hit escape and exit. I am trying another flight tonight with it to see if things have calmed down. If I don't get a freeze, I will be happy. If I do, I will try and see if anything obvious happened beforehand. 

2 hours ago, GoogleTrEx said:

Would there be any log files anything that could help sort out what is going on? Would eliminating all keyboard keybinds maybe help? I don't use they keyboard except to hit escape and exit. I am trying another flight tonight with it to see if things have calmed down. If I don't get a freeze, I will be happy. If I do, I will try and see if anything obvious happened beforehand. 

I completed the flight without any hangs. The only thing that was different (Besides the fresh install of MSFS) was that I set mouse, keyboard, and my collective to "Default" control settings and made sure there weren't any "autopilot" related control inputs on any of my controllers except AT and AP disengage keys. I will post here if it hangs again and I can add any new details to it.