I am building with the release version of Xcode 7.0. No storyboards, just nib files.
I have a single UINavigationController created by the app delegate
I was finally able to track it down to a UIActionSheet class variable inside a third-party library, Mapbox GL.
I opened an issue with that dev team: https://github.com/mapbox/mapbox-gl-native/issues/2475
Partial credit (and an up vote and bounty) to @Aaoli for mentioning having a UIAlertView as a class variable.