That covers half of what I said. Without the other half, using diplomacy to form alliances against stronger adversaries, snowballing is inevitable. Wars lasting 15-20 days are ridiculous; it should take most of that time just to bring the armies up to full strength and gather for a campaign. Assaults on castles and towns should be devastating, and require time for the besieger to recover afterwards. Running home and conjuring up another 50-100 men from willing volunteers should only be possible once or twice; after that, you're either taking away your own castle garrisons or stripping the villages of peasants to work the farms, and recovery of that lost manpower should take a significant amount of time, not a couple of days. Once a faction has used up its "excess" manpower and starts dipping into productive workers, it should attempt to end its current wars, not start another.
Actually, I'd love to see a faction strength mechanism used for bandits as well. Initially, the bandit parties would be small and weak, but fast and hard to catch for a sizable army. If not kept in check, they have the potential to gain strength over time, and you'll see larger bandit parties capable of taking on patrols and often winning. Eventually they'll reach a size where they're not fast enough to outrun some of the faction armies, and the bandit faction strength will then get cut back quickly, once again leading to small parties that are hard to catch.