To be honest, the beauty shop people think bleach and redye is a horror story because of the condition it will leave your hair in. They get taught not to do or advise it at college so they simply won't do. My hair is naturally medium brown and they told me the same thing, permanent dye after bleach will "rip my hair out", however, I have bleached and redyed 4 times now and may even do a fifth.
How is your scalp and hair feeling? The very back/bottom of my hair by the nape of my neck is like wire, becasue this is always where I started the bleaches so it is the area that had it on for longest, but it is only a tiiiiny section of hair that feels this way, and after the fourth bleach and redye my scalp hurt for a few days.
Don't get me wrong my hair is in a bad condition now, it has split frazzled ends, is tangled, and even after deep conditioning treatment it is quite dry, but damage is the name of the game here and if your hair feels OK I really really can't see it falling out.
Another thing, I was told that the hair they took would be cosmetically unoticable and they would be sure to take it from the back/middle of my hair. Becasue of this I clipped the front of my hair out of the way and left it out of all but the first treatment in order to keep some good hair in the most visible place.