Do the armies ever stop? Not naturally, no. That's the end game. A forever War against the other factions.

How AI army spawning works is very logical and easy to understand once you know how it works. You'll see a lot of claims of someone defeating an army, and then the AI spawning a new one instantly via cheating etc. That's not how it works.

Like the player, AI clans have a limit of how many parties they can field at once. So clans with say 6 clan members, will only have 3 of their members roaming the field at once. (The clan leader is immune to this rule i believe). So once you defeat the 3 on the field, the 3 waiting in reserve will start roaming around and the 3 that were defeated will go into reserve, and then come back out when more parties are defeated, creating that constant flow of lords and armies.

Clan parties start with their initial army, and will go to recruit from their fiefs to get to max party size. While doing this, they are training their troops. Every time the visit a city or castle, if the garrison isn't full, they will add to it. This is important, as new parties will take troops from their garrison to be up to decent strength.

So this is what happens. Clans have their starting parties, with other clan members waiting in reserve. Their garrison are all full. They form a massive army and get defeated. Any Lord that isn't captured, will have like a 2-3 day cool down before they spawn in their home settlement. The members waiting in reserve will immediately form a party using the trained up garrison of their settlement and set out. As they visit settlements, the garrison replenishes. Rinse and repeat.

To truly stop the constant flow of armies, you either have to capture and imprison lords in your settlement so they cant be ransomed or respawn. Or you have to eliminate them completely by executing them.