Independent councillor Colin Brewer made the comments to Theresa Court, who works for Disability Cornwall, while she was manning a stall at the County Hall in Truro in October 2011.
Despite facing calls to resign, he remained defiant over his right to remain in his councillor role and gained 335 votes, beating the Lib Dem candidate by two votes.
He wrote a letter of apology to Theresa Court and said at the time: "I have no intention of resigning. I don't think I have done anything wrong. I have apologised."
Theresa Court told the Huffington Post UK earlier this year it was "quite frankly an insult that he had to be told to apologise after a year and a half."
She said the manner in which the letter arrived was like he was making a stand, with "a second class stamp and folded into no less than eight pieces."
Disability Cornwall said on Friday they are "shocked beyond words" and that it was "truly a sad day" for Cornwall.
They said in a statement "Colin Brewer has never contacted Disability Cornwall since this incident became public knowledge, or in any way tried to make amends for what he has done. He didn’t think he did anything wrong and put his comment that ‘disabled children should be put down as they cost the council too much money’ down to a ‘flippant remark’."
Brewer has given various explanations for his behaviour, telling the BBC "I said they should be put down. I was just hot under the collar, I suppose, coming from a council meeting where we had been talking about budget cuts and staff cuts.
"Sometimes people can just catch you on the wrong day.
"It's not a good enough excuse, I will forever be apologising for it. I can't apologise enough. It's not something that's in my nature, I always support disabled charities.
"I am very sorry."