Linda, yes I have noticed breakage. I use those little thin bands and they say they don't cause breakage (but they are meant for human hair, which I think is stronger than the Havanese hair). Part of it is caused by Augie rubbing his head on the carpet, causing matting, and then there is some breakage when I comb it out, even though I try to be extra careful, using corn starch, and pulling it apart before combing. Also, at first, I accidentally cut some of the hairs when I was cutting the bands off, so there are short pieces that seem to be incredibly slow in growing out. In one of the threads on here, someone mentioned a technique using papers (like used in giving a permanent, I believe) to wrap the hair before applying the bands to prevent breakage, but I haven't tried that.
I know that everyone says they see breakage, but I truly don't! It might have something to do with the fact that Hitchcock has a TON of hair, though. He wears a top knot every day and I use the Goody Ouchless bands.
Rosie definitely had breakage. So much so that I haven't put up a top knot in months. I just had her trimmed in March and the groomer trimmed the head hair that was still long to not fall in her eyes. It is slowly growing out; but so delicate the hair is. I probably will never do a top knot again unless the texture of her head hair matches the rest of her body--enormous amount of hair.