Kindle Fire - Flickering UI on 2nd camera

On a Kindle Fire SD only, we have an issue where our user interfaces sporadically flicker (it appears to not be drawn during some frames). This issue does not apply to newer Kindle devices, nor any other Android devices or iOS devices.

The UI is built with NGUI using Transparent Unlit shaders, using a UI Camera that is orthographic with depth=1. The main camera is depth=0.

When flickering, any elements that lie underneath the Kindle's menu bar's semi-transparent bar are rendered correctly (and are updating correctly every frame).

Minor changes in the scene geometry seem to affect how often or how fast the flickering occurs, but simply adding or removing geo does not remove the problem; it just makes it happen at different times. Certain camera angles with certain combinations of characters tend to create the flicker more often than others, but we haven't found any correlations with the flicker.

The flickering does not happen consistently or at a consistent rate. Camera movement and animations do not seem to affect the flickering.

The flickering is not a performance stutter -- characters and scene animations are moving smoothly.

Shaders don't seem to be the issue - changing to Mobile/Diffuse without any transparency doesn't change the flickering problem.

We tried enabled vertical sync -- no change in the flickering.

Any suggestions on how to further investigate the problem?