I've done some research on the question and found this, but unfortunately those questions refer to a Cold war.
This war in my question is very hot indeed, a stalemate that's lasted over a decade with both sides fighting on the same front lines since the war began. Casualties are countless and neither side is willing to surrender.
This world is Earth in the year 3000. SEDA is the first faction, GRP is the second.
SEDA takes up most of Asia and Oceania, and the Western half of South America.
GRP takes up Russia, Africa, and the Eastern Half of South America.
New Venice is a neutral third country, located in what is now Hawaii.
Abandoned areas comprise Europe and North America, as neither faction lays claims to these lands for one reason or another (resistant locals or large amounts of radiation)
These two factions take up most of the world. Each of these is made up of a number of smaller nations, but effectively they function as a single political entity.
It would be in the interest of both factions to claim the nation as their own, adding the island's production and manpower to themselves and utilizing it as a potential jumping-off point for any future invasions.
However for whatever reason they choose leave New Venice completely self governing. I've looked at real-life instances of neutral countries being left alone by a hostile force, but so far the reasons I can find that resulted in them being left alone don't really apply to my world.
A good example is not wanting to antagonize the rest of the world. In this scenario, there isn't a rest of the world to antagonize. Both sides are at total war, and the relationship can't degrade past that.
The solution doesn't have to be permanent, it just has to last for at least a decade.