Dad Tony, from Castledrum, Keel, Co Kerry, said that doctors are happy with his progress and are hopeful ahead of the crucial six month check-up.
"Liam is doing really well. He's off the anti-seizure medication," Tony said.
"He has had some staring episodes which could be seizures. But doctors think it could be daydreaming."
Now Tony is preparing to leave the country for work, which he said will be painful.
"I stopped working 15 months ago. I'll return to work but I have to go overseas for this as I'm a ship's captain so I'll be in Oslo," he said.
"I'm going to be away from Liam and Mary and from Saoirse's special place, her grave here," he added. "It's not going to be easy but I refuse to live on handouts."
Tony and Mary lost their daughter Saoirse (5) to the rare neurological disorder, which affects a sufferer's speech and motor skills and can cause seizures and blindness.
And Tony said that the little boy, who was three in July, misses his sister desperately.
"He sees photographs of him and Saoirse and he asks about her. He's always blowing up kisses to the skies," Tony said.
"When Saoirse was sick she was quite upset because she thought it was her fault that everyone was crying. So Mary said that it has to stop -- we have to be positive."
The Heffernans are hopeful about the future and Liam's physiotherapist has noticed an improvement in his mobility.
"He's coming along really well," Tony said. "He will have his full check-up in three months. We're going to leave for New York at the end of October."
Local firm The Interiors Directory has pledged that for everyone who signs on to their mailing list at www.interiorsdirectory.com, they will donate €1 to the Saoirse Foundation for Batten Disease.
In addition, they are hoping to get to 50,000 followers on Facebook as one anonymous donor has pledged a donation of €50,000 when they reach this.