Just adding this in... I work in a lab, and we have to use distilled water for quite a few procedures. It is processed in a sterile bottle, and you open it only when you need something. Even after months of a bottle of distilled water being opened like this for procedures, and coming into contact with the air, it still has mineral content right at zero. The contamination due to air is primarily about encysted bacteria that might be in it. The no-bacteria benefit of distilled goes away within a couple days of exposing it to air; probably less when exposed to solid sources of contamination (like a frog!). I've run experiments on exactly this; when exposed to air, distilled water only takes about 24 hours longer than untreated tap water to begin growing bacteria, and is almost exactly equal to bottled spring water.

In regards to the frog; I really don't see the water being the cause of such a profound growth problem. I may be wrong (really I'm just curious about what's going on here) but I think you would see problems other than just stunted growth if this was conditions-related. Like bone deformity or profound weakness, because the frog's body would still be trying to grow. This frog's body doesn't seem like it's making the attempt to grow.
I'd say make an extra effort with keeping this one eating regularly though. Normally I'd say not to worry about a yearling going under for days at a time, but I imagine this guy's feeding schedule is more like a baby frog?