How is it falling out? Is it by the roots or is it breaking off?
If it is falling out by the root, then it could be an autoimmune/nutrition issue and you should probably see your doctor to get blood work done and establish a cause. Taking some hair/skin/nails pills could help and try not to put conditioner right on the scalp. Hair loss can also be caused by not rinsing out some conditioners properly. I know it is an old myth that conditioner softens the roots and causes hair loss but it cant hurt to try this. I have used joike k pak and hadnt had any issues, i dont use it on the scalp though, only the damaged ends.
If it is breaking off then it is most likely damage from the dye they use on your hair. Do they re-dye all the hair or only the roots?
Of course, it could be a combination of things so safest bet is always to go to the doctor, especially since you said you are very ill.