> And while many religions teach that God intervenes in human affairs, none of them, as far as I know, believe that he responds to whining. (Would you worship a god who does miracles if you just annoy him enough?)
It's not exactly as you say but it's roughly how I interpreted the parable of the unjust judge.
That parable came to mind immediately. There is in fact a god that labels unanswered nagging as acting unjust. A lifetime ago in seminary I knew a guy who rage quit after spending months contemplating the implications of that passage and observations about how common it is to see others unanswered prayer. Don't know what happened to him but he would just mutter that his beliefs didn't matter since "jesus defacto makes the claim he is unjust and defeats himself", the problem of suffering indeed.
It's not exactly as you say but it's roughly how I interpreted the parable of the unjust judge.
https://en.wikipedia.org/wiki/Parable_of_the_Unjust_Judge