Jack's father Cameron, who spoke to the Herald on the condition the family's surname was not published, said he and wife Elena would postpone birthday celebrations.
They would mark Jack's birthday when he was a bit better and able to enjoy it.
"He's not talking at the moment. He is stable, but he's getting a lot of shakes in his legs and arms. His eyes twitch as he tries to focus. There's not a lot of change," Cameron said.
"They're trying to get him to sleep normally, but the twitches wake him up so he only gets 15 minutes at a time."
As a result of being deprived of oxygen as he choked, Jack suffered damage to his brain. Doctors are yet to establish the degree of damage.
A spokesman for the Government's labour service confirmed an investigation was under way.