Distilled water is collected by gathering steam, you can actually distill it yourself. The problem is that it is completely devoid
of nutrients so if it is used in an aquarium it really
needs to have the vitamins and other such things added back to it. Distilled water is generally free of chlorine, anyway. The issue could be a combination of lack of heat and lack of proper nutrients available in the water.
Distilled and deionised water (very similar) are often used in car batteries and irons to stop limescale building up -- it really shouldn't be used in an aquarium unless you have a very fussy animal in there (I know some people who keep select species of shrimp that use 'pure water' (usually reverse osmosis water) and add nutrients/vitamins/minerals etc to it in order to maintain a stable pH/GH/KH as the species of shrimp are extremely delicate) and know exactly what products to add in order to regain the levels of nutrients required by animals and plants to flourish.
Tap water with water conditioner is, in most places, perfectly fine to use
I'm glad to see that the fish has improved.