If I understand the proposal correctly, I see these potential problems:
1. When the daytime arena shuts down, the 2 nighttime arenas must be clones of the daytime arena to let every player resume the same game, albeit in 2 different arenas.
Imagine the whines when i.e. one chesspiece is dominating the war, then the arena shuts down, one arena saves the status quo and the other appears in default form. Now, when the playerbase moves in the 2 new arenas, probably 50% of those chess-pieces that dominated earlier on, find themselves with their efforts erased. I could imagine this as pretty frustrating experience.
2. If those 2 arenas are really clones of the previous one, then the problem above might not appear, but essential the actual choice between the LWAs is removed. We will always have the same maps in both arenas, and in many cases the actual state of war will be very similar, at least for a good while after the split.
3. Lets say we stick to the clone theme, and let the state of war evolve in both arenas. This could mean that the sate of war in one arena is vastly different than in the other. Now the time comes to merge both arenas into one again. Which state of war should be carried over? Arena A or arena B? No matter which one is chosen, there is a big chance that again 50% of the playerbase are dissatisfied that their efforts got erased.
Basically, I see chess-piece loyalty as a major obstacle and also fairness is most likely not guaranteed, unlike the current setup, which is pretty solid in this term.