Hi Elefvee
Many people are drinking sugar-free diet drinks on fast days. They are not specifically forbidden but Dr M has said he is against the idea. I am not sure how much scientific research has been done on how the body treats these drinks and much of the research that has been done has been sponsored by the soft-drinks industry!
In my opinion, it is worth trying to avoid/cut down on them because a) we don't know what the effect on the body actually is and b) they are expensive! However, having said that, if I found they helped me get through the fast day, I would not worry about having them, just maybe consider whether I could cut a couple out?