I don’t know if this is the same issue or a separate issue, but my A320neo (both stock without any mods and the A32NX) also veers off course when on AP. It doesn’t seem to matter whether it’s in heading mode or NAV mode.
Really frustrating and I’m surprised there aren’t more threads about this seeing how often this happens to me. I’m beginning to think it’s because of something specific about my system.
I’m flying with keyboard mouse and xbox controller. I’ve tried setting the deadzone to 5% and sometimes it seems to work and sometimes it doesn’t. I’m thinking it’s not really about the deadzone, it’s simply about pausing / unpausing or making a change to the settings and resuming flight. Sometimes I can get it to start working again by enabling and disabling “LOC” on the dashboard or by generally fiddling about with the AP settings.