I can't think of a reason either, which is why this is weird…but true.
I tried the physics collision matrix, but no effect. Here are some more specifics that might help figure it out.
The spinning cube is part of gameplay and not the UI, and actually doesn't spin. My gameplay camera actually spins 90 degrees around the stationary cube when I swipe. My NGUI camera only renders NGUI objects, and my gameplay camera only renders gameplay objects. So to be more accurate, when I spin my gameplay camera twice, some of the NGUI element box colliders get disabled. And interesting to note that spinning just once does not disable that same component. My UICamera Event Type is set to 3DUI, and I do NOT attach UICamera script to my main gameplay camera, only my NGUI camera.
I've also noticed that other random NGUI components get disabled during runtime, like UIStretch and UIAnchor. All the NGUI elements look right, but those components are also getting disabled somehow during runtime.
I'm using FingerGestures as input, so maybe that input is affecting NGUI somehow, in addition to the gameplay.
And my own gameplay camera script uses a StopAllCoRoutines() call as part of the spinning process. So if NGUI uses coroutines, maybe that's what causes the random component disablement.