In 14.3, the only way to keep it connected in my Apple TV is to NOT use the apple remote, the moment it connect, the Dualshock stop working (stays connected but it doesn't control anything). The system recognise it and if you go to the controller settings, you can identify it and the controller vibrate, but anything else isn't working (you can't navigate or use it in any game/app). It seems like a bug. Also, you have to unpair and pair every time you want to use it again. It doesn't happen on my iPad (13.2.3) where it connect immediately if I hit the PS button, if I've paired previously with the device. So it seems like another bug.
So the steps to make it work are:
1) Start Apple tv or reboot (not suspend). Once it's started, do not use the apple remote to navigate, instead you need to use another remote (like the tv remote or another remote controller, since the Dualshock doesn't connect automatically).
2) Unpair and pair the Dualshock.
3) Now you should be able to use it.
Topic:
App & System Services
SubTopic:
Core OS
Tags: