When I got their approval email a week or so ago, I’d assumed that it was approved for all devices. Well, I was wrong. They were still testing it on the Kindle Fire, and they let me know today that it had been rejected. The exact text of their email that explains why:
Neil Rajah (Free) was found to be incompatible due to issues with the app’s interaction with Kindle Fire’s Settings bar. Neil Rajah (Free) stops playing background music when users access the Quick Settings (e.g., adjust the volume).
Neil Rajah (Free) was found to be incompatible due to issues with the app’s interaction with Kindle Fire’s hibernation feature. Neil Rajah (Free) stops playing background music after the device hibernates and then is woken up.
I started typing out an email telling them it was ‘by design’, but I should be honest here, I cut some corners, and their test team caught it. Have to give them credit for that 
I think someone in my beta testers had pointed that out as well, but I forgot to add it to my to-do list, and then it fell through the cracks.
Technical Stuff
In all my previous games, I never paid attention to pausing audio when the game was paused. If you restarted the game, the audio resumed immediately. This is poor design, as this article explains. Quoting:
I’m on the bus to work, passing the time with a great Android game. I’m completely entranced by whatever combination of birds, ropes, and ninjas is popular this week. Suddenly I panic: I’ve almost missed my stop! I leap up, quickly locking my phone as I shove it into a pocket.
I arrive breathless at my first meeting of the day. The boss, perhaps sensing my vulnerability, asks me a tough question. Not tough enough to stump me, though — I’ve got the answer to that right here on my Android phone! I whip out my phone and press the unlock button… and the room dissolves in laughter as a certain well-known game ditty blares out from the device.
That’s exactly what Bus Jumper would do. With Neil Rajah, I do a slightly better job. When the game pauses, I pause the background music. But I don’t always resume it at the right time. So depending on what you were doing when you paused the game, you could come back to a running game that has no background music. It’s not permanently broken, the music will resume when you get to the next screen, whatever that might be. But I’ll have to admit, that’s not the best user experience.
So now I have to figure out how to fix it. The article linked to above gives a few possible solutions. I can implement that fairly easily for the main game screen, because there’s a clear way to pause and resume that, and I already have the buttons. If you’re in one of the menu screens, I don’t really have the concept of a paused menu screen in my game. They’re always paused, in a sense, since they’re static. So I’ll have to figure something out for that.
And then re-submit to Amazon, and wait a week or two for the testing. On the plus side, this explains why I’d had exactly zero new users from Amazon (I’m using a unique version number for that store, so I can track it separately from the others). This tells me that the only people browsing apps / games on that store any more are Kindle Fire owners. Anyone with a regular phone or tablet that has the Google Play store, is using Google Play. No real surprises there.