This bug seems to repro very inconsistently for me, but I've seen it affect Atmospheric Fog and Exponential Height Fog, and reproduced in 4.18.3, 4.19.2, and Main CL 4093338. I've attached Config files and video from license.
Per Licensee:
We're currently using height fog in our game have noticed something very strange during the split screen mode. It seems like that if player 1 isn't looking at the fog object in the game, player 2s fog doesn't render?
Result: Fog will pop in an out of view similar to attached video from licensee.
There's no existing public thread on this issue, so head over to Questions & Answers just mention UE-59663 in the post.