Symptoms sound very similar to a febrile seizure my infant son had once. I wonder if the infant was also fighting an infection. Very scary stuff, but a febrile seizure is normally ultimately harmless. I can't imagine what it would be like to not be able to immediately get help though.
Actually no, it sounds very much like heat exhaustion and potential heat stroke. The article says as much: the child had no underlying conditions.
Febrile seizures are usually harmless, true, but this is worse. Heat stroke is potentially deadly, and infants are particularly vulnerable to it as their ability to regulate temperature is much less developed than in adults. The article says it was 90 degrees in the shade and who knows how hot in the aircraft. Those are potentially dangerous temperatures for a small child.
http://www.nhs.uk/conditions/heat-exhaustion-and-heatstroke/Pages/Introduction.aspx
The air crew did all they could, from the sound of it, and followed good procedures for heat exhaustion for anyone who isn't a medical professional. I don't think more could be asked personally of them. The problem is protocol. From the sound of it, they had two levels of escalation: taxiing to the gate for serious but not life threatening medical events, or stop and bring the ladders and a medical team for life threatening medical emergencies, like I imagine they would in case of a heart attack.
For whatever reason they thought this wasn't an immediately life threatening event, which is not something I'm sure I agree with if the child really was lapsing in and out of consciousness. Those are symptoms of severe heat stroke. They should have been taken in an ambulance sooner - it should have been clear by then what that was being done to cool the child down wasn't enough.