Configuring Sabnzbd server in NZB360 android
If I use my external IP address, it works.
But if I substitute the domain name it does not work.
I know the dynamic DNS is working because:
1. when I ping the name, it returns the correct external IP
2. when I remote into another external computer and use the browser, it works.

I was just about to post this and I thought about one more thing.
I restarted my phone and it worked.

My theory is that it was caching the DNS entry.
This occurred to me previously and I had already tried to clear cache in the application settings.
Apparently in the chrome app, clearing the cache does flush the dns cache but does not appear to work that way in NZB360.

As often happens, writing the question down leads me to the answer myself. Posting so it might help others.