Sounds like the dismissal of the permission dialog retriggers the onResume of your Activity/Fragment. In that case, it would make sense that checkPermissions() gets called and you are stuck in the B branch of your code as the shouldShow...Rationale will only fire once as @Edric confirmed.

You can override onPause() to verify this.

"But I want to support a "corner case", whereby the user continues to refuse until they give up and delete the app (I know, I know, bear with me here...)"

This sounds like you would want the infinite loop that you are getting?

What is exactly the problem with the behaviour you are seeing and what is the behaviour you are looking for? Do you want to show the explainDialog on a loop instead of the requestPermissions dialog?