I think short bows can be accurate, but usually that means you must shoot longer arrows. My main problem with shorter bows is that I can't come back to my familiar anchor point, so I feel as though I'm kinda floating around in space. I prefer a longer bow because I can hit my anchor point. A shorter bow can't be drawn as far, and I think because of that you can't lock into your anchor. When you shoot a longer bow, your anchor point almost acts as a "lock" to help stabalize your body and any addfitional movement that might occur. As you draw your bow, both hands are away from your body, which is a more unstable position. As your hand gets to your cheek, you now have one hand close to your center of gravity, which helps counteract the fact that your other arm is extended.
At least, that's the way I feel when comparing a short vs. long bow.