I really have two thoughts on Itachi's illness.
The first being that his MS may have been connected to his body for too long. The MS might secrete some sort of poision that only does damage to the original owner over time. No one has ever had Their MS in their body for that long, other than Obito who has part of a zetsu essentially keeping him healed all the time so it doesn't effect Obito. Itachi on the other hand has had his original MS in his body for many years with nothing but medicine able to stop the poison it slowly releases. This poision would stop when a person goes blind from using their mangekyou sharingan too much or when eyes are exchanged, this would explain why we've never seen anyone else with such an incurable illness (as everyone with an MS haven't had their original MS for long enough for the poison to be deadly to them).
The other thought of mine is that we all know that Itachi has extremely low chakra reserves. Low to the point where he doesn't want to use amaterasu/tsukuyomi more than once or twice a day. Excessively pulling out so much of his chakra from his already low reserves so fast might hurt his body/chakra network. We know that damage to the chakra network is extremely hard, if not impossible to repair and that damage eventually became so great that his organs weren't operating correctly without medicine to force them to work.
