When I play as Germany, Italy seldom joins the war on their own account. Why?
Why should they? With the French and British navies still intact they can't really function and when Germany gobbles up Yugoslavia there ain't much left to conquer. Okey, I'm not sure if the game is programmed to behave like that.
However, Italy was actually quite reluctant to go to war. Mussolini had at least some grasp that Italys armed forces wasn't ready for their British counterparts. And even if they had done better, Italy didn't stand to gain that much of a war. These points are still valid in the game, so it's only natural for an Italian entry in the war to require a bit of German persuasion.