Minecraft 16w05a, Minecraft 1.9.1, Minecraft 1.9.2
(Pretty sure this has been a bug for years, but have not checked.)
Here's a video of the bug in action:
There's a beacon just at the edge of my render distance; I can see it, but only when it's not near the center of my FOV.
In any case, my expectation is that either (1) object appearance through the fog does not change as you move your head or (2) objects are more visible when looking directly at them. But making objects less visible when looking directly at them is counter-intuitive (and also now how human vision works).
(This bug is more noticeable in the Nether, where fog/lighting make the effect more pronounced.)
After talking to others, I think maybe the 'back plane' of the view frustum is just too close? Given that the chunks outside the render distance are not loaded/rendered, as a layman I imagine you could just increase the distance to the backplane (this would not cause undue extra overhead, as the faraway objects are implicitly culled by virtue of being out of render distance?). (Also, the backplane is a function of the render distance; I get this oddity even at render distance 10, even though my machine can run fine at render distance 20. So it seems surely when I'm at render distance 10, it could put the backplane as though I was at render distance 11?) I'm not an expert here, so maybe I'm missing an important detail.