Braces and short roots - how big are the risks of getting braces a second time? (photo)

I had braces when I was younger but they have moved and I really want my front teeth straightened again. I've had one dentist say I can't have them due to my short roots and a special orthodontics say I can but I need to be aware of the risk of my teeth falling out. How big is the risk or is there another procedure I can have instead?