Is it actually falling out as in balding or is the hair in those areas just really short? I know that LC blow their coat. I actually read somewhere (can't locate it now ) that a LC chi can loose so much of it's coat that it can look as smooth as a SC but the hair will grow back.

if it is actual balding maybe she has a flea allergy or something. Unfortunately(but fortunate for us) we do not have that problem. I only bath Chopper with baby shampoo and I use no flea preventative unless I happen to spot one.