I had this exact thing happen with my two month old Pomeranian goslings last month. The first seemed fine at 2 pm and was found dead at 5. Another looked drunk the next morning, so I put him in their house with food, water with vitamins, and gave him a shot of Tylan. He didn't improve by lunchtime, so I began holding him in a towel and giving him some Denagard water with a syringe. He began having convulsions and ended up dying within an hour. The closest vet that will look at them is in Baton Rouge about an hour and a half away and they weren't in since it was a weekend. I called, but all the number did was route me to the on-call emergency animal hospital that does not do these sorts of animals.
When I went to bury the second one that died, I noticed yet a third with the same symptoms. This time I immediately began the Denagard water and doubled the Tylan dosage. I had looked up the symptoms and determined it was most likely some sort of toxin they had either ingested or were breathing in, so I began thinking. I know I have no plants that are toxic to animals (was very careful about that). I had not changed their food and it had not gotten wet, so I took a look at their house and the fresh straw bedding I had put in the night before the first death: I mucked out their house...then bleached it (paver stone floor over sand). I also disposed of the clean straw I had put in the guinea pig cage I use as a hospital and replaced it with some of the guinea pig's Carefresh bedding.
Sick gosling number three made a full recovery within hours: It literally went from wobbly with diarrhea to eating, drinking and yelling to get out of its cage. I was able to return him outside the next day after I determined that nobody else was sick.
In the end, by process of elimination, I determined it was the straw bedding in their house making them sick. I had changed their bedding the night before the first death: It was a new bale I had not used from before and did smell a bit off...not moldy, just not right either. After their house was cleaned and disinfected I aired it out and used bedding from our horses hay, which is very clean and fresh smelling. Their house has very good ventilation, but I guess being closed in and walking/laying on the hay must have released some sort of mold spores. I will only use fresh smelling hay from our horse supply from now on. If it smells good enough to eat, then it is good enough for my geese to sleep on.
So, the best advice I can give you is first, get them started on some meds and then think really hard about anything new you have introduced or plants they may have found in your yard. Have you or any of your neighbors fertilized or used an herbicide..you know....things like that.
Good luck and I really hope your baby made it and you find the culprit.