So I am having this exact same problem with my AA+ and AVX mount. The explanation here in this thread is spot-on and perfect! I did open a ticket with ZWO about this yesterday not expecting it would be addressed. But after reading this I have hope. Like the rest of you I have upgraded the firmware of everything to the latest. Celestron CFM was a couple days ago and included new firmware to the electronic focuser on my EdgeHD8. My AVX is pretty new from Nov 2023 and the AA+ is obviously up to date.
I even tried using IP as a connection on port 4030 and it seemed to work. Until I tried focusing, then it dropped just like the serial baud connection (I was using 9600).
Like you guys explained above, I don't need the autofocus, I just need the connection to remain after using the AVX HC to focus. And yes I can reboot everything like you all said, but it is really a kluge.
So I guess I'll hang out in the forum for a bit to see if I can fix this situation.