Civilization – Stop two allied city-states from war

If you kill quite a number of units of a city state and/or keep trespassing on their territory enough to get your score very very low over an extended period of time, they eventually will be convinced that you are so evil it's not worth considering peaceful coexistence, so they will be in perpetual war with you. You will not be able to buy their friendship and relations will not heal by themselves over time.

Actually that doesn't mean too much, though. If you go near them, they'll attack you, and if you leave cities undefended near them, they'll capture those. Apart from that, they won't hunt you across the map and they won't make others hate you as well. If you just leave them alone now and make their area taboo to your units you can still get along with the other city states just fine.

You might choose to have one perpetual warring city-state next to your army outfitter because city-state units train your troops longer than barbarians do.

1. They can be significant threats, especially if there are enough of them against you. The game always ensures that their units are upgraded to the same level as the player with the highest tech advantage, and they are able to produce units pretty regularly.
2. They will leave their borders and are even capable of taking over enemy cities, although such an occurrence is infrequent.
3. Nation states can get to a point where they permanently declare war on you. This makes the diplomatic victory a lot more difficult since you can't rely on their votes. You also lose out on resource trading potential, which can be quite profitable.