I've waged a battle with my hair for about 4 years now. I take a form of Chemo therapy and have frequently toyed with cutting my hair and decided against it. I have it trimed and clean up the ends but I don't go for a short cut. It might ease up on the long hairs on the floor, brush, bed etc but it won't stop it from falling out. Each time the dose changes the falling out increases and then it settles down. I make sure I use a good conditioner. When it is bad I don't wash it as often as the hair is weakest when wet and the natural oils are better for it.
However, since it's our hair we notice the loss more than others do.