If you are going to take the capital (especially if that is that empire's primary or sole European province), you probably should prepared to go ahead and finish them off. Rationally, the AI has nothing to gain from a peace (it would still be at the mercy of every other power and cannot "win"), unless you are offering them the capital back.
Alot of human players, if faced with this circumstance, would simply conceded the game and start over. The AI, of course, does not have that option, so them trying to a last ditch effort to regain key territory is not unreasonable. Barring total conquest, a power has to perceive advantages to accepting peace over its current state of war, and this is generally as true in the game as in real life.
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