This is verry odd. I can connect using my duckdns.org subdomain from my laptop and mobile (using WiFi) but only if my mobile is conected to my local network (if I turn off WiFi and use mobile data it will not connect).
Recently I canged my router. I have the router I was given my my ISP (British Telecom) and a TP Link one conected to it (the one I connect my mobile and laptop to).
I have a port forwarding set up for both for 8123. This is what I previously did with my previous simeler setup with the suplied router and my old Rock Space one. So it works if I conect to the BT or Link one wit the full URL but not if I try to conect using mobile data (mobile data is working fine for everything else).
The Pi With Home Assistent is conected to the Suplied BT router with a wired conection.
Just to reiterate the same port forwarding worked fine with my previous router.