I have the TM Airbus stick and just tried a flight with Autopilot and didn't have a problem when selecting Button 3, or button 4. Button 3 for me is "Reset Cockpit View". The A/P stayed connected.
Just to confirm, when you Filter for "Assigned" and click to "Search by Input" and push your button 3, does it look something like this? There is nothing else that comes up?