The Iron Man 3 prequel comic already explained War Machine's absence from the first Avenger movie as an assignment against Ten Rings terrorists in Hong Kong. You can't conveniently have War Machine be "away on assignment" every time the Avengers get together to save the world.
War Machine is part of the comic-book Avengers, so he has every right to belong to the movie Avengers. In fact, it makes absolutely no sense that the Avengers *wouldn't* try to recruit him --- whenever they're trying to save the world from a supervillain that requires teamwork, they're going to need all the super firepower they can muster.
It would've been really nice if they had shown a little of what is in the prequel comic in the movie, even if it was just conversation between Tony and Jarvis inside his helmet, Jarvis could've relayed Rhodey's whereabouts. Going forward they are going to need to address War Machine when The Avengers rolls around, even if it is just a quick cut-away scene that shows War Machine in battle against a portion of the antagonist.