I have the same problem in my project, in splitscreen.
It seems that the fog is getting disabled when the source (The Sundisk) is not in the player’s viewport anymore, and it pops back on when it is…
It reminds me of when you sometimes have particles that do not render if you do not have the particle system’s origin (emitter) in the viewport.
No solution yet, but it’s definitely only in splitscreen mode.
There is definitly a problem/limitation when it comes to atmospheric fog and splitscreen mode. If you add a second local player in the multiplayer shootout project the sky turns black.
I had a similar issue, where in splitscreen mode, and only in some levels, the sky would randomly get completely culled and turn black for one player. I found out by accident that this bug only occurs when sg.PostProcessQuality is set to 2 or 3, so I looked into what specific values this was setting, and narrowed it down to r.LightShaftQuality.
Seems like an engine bug with r.LightShaftQuality interacting very poorly with AtmosphericFog when using splitscreen.
Setting r.LightShaftQuality to 0 completely fixed this problem for me.