Here is some more info to recreate the problem.
1.) If the app "loses connectivity" with the last connected Roku device, while on the app Remote screen, the app hangs with a spinning cursor screen documented above.
2,) This usually occurs after the mobile is turned-on after being asleep for a while.
3.) If the Roku app is left on the Home screen before the the Mobile device is put to sleep, the problem does not occur. The app just reconnects to the last selected Roku device without problems.
4.) Putting the Mobile device to sleep does not affect other internet related apps (browsers for example).
5.) The prior Roku app just ignored touches when left on the Remote screen, but did not hang. So this is an annoying regression of a prior issue with the app.