@stoney66 Thanks for that.

I had a look at those cfg files and they all looked fine.

So I did a completely fresh install of RetroPie.

Tried it out, R-Type controls worked fine.

Then I started adding nice tweaks such as ES Themes etc, and suddenly R-Type had the same problem - P1 right not working unless I re-configure the MAME2003 controls every time.

Not sure what change I applied that caused this, so I'm going to do it all again step-by-step and see when it reoccurs.

My gut feeling is this is a bug in the Pimoroni Picade HAT drivers.