Lynda Roughley offered to resign on Tuesday evening after her boss was forced to admit during a live radio interview that the claim - carried by his official website for six years - was wrong.
A party spokesman said Mr Nuttall had rejected the offer on the grounds that she should not lose her career for what appeared to be a “minor error” after years of loyal and effective service.
Ukip’s main financial backer, Arron Banks, hit back at opponents who have criticised Mr Nuttall over his comments about the 1989 football stadium disaster.
The millionaire donor used Twitter to accuse them of “milking a tragedy forever”, adding: “I’m sick to death of hearing about it. It was a disaster and that’s it, not some sort of cultural happening.”
Families of some of the 96 Liverpool fans who died at Hillsborough voiced their anger at the false claim.
Barry Devonside, whose son Christopher, 18, was among the victims, said the Ukip leader’s credibility had “gone out of the window”.
“It’s insensitive. We are still awaiting the decision of the Crown Prosecution Service as to whether charges will be brought and we don’t need this kind of thing from Paul Nuttall,” he said.
“He should know better as a politician and leader of Ukip.”
Hillsborough Family Support Group chairwoman Margaret Aspinall told LBC radio: “A lot of people who were there that day did lose close personal friends and I think it’s an insult to them as well as to all the families who did lose somebody on that day.”
Mr Nuttall apologised on Tuesday for the claim - contained in at least two press releases on his website - after being challenged during an interview with Radio City Talk in Liverpool.
He told presenter Dave Easton: “I haven’t lost a close personal friend, I’ve lost someone who I know. I haven’t put that out, that is wrong.”
In a statement later, Mr Nuttall, who is standing for Ukip in the Stoke-on-Trent Central by-election, said he was “appalled” when he found out what had happened.
“This was an article that I did not write and did not see prior to it being posted by a member of my staff.
“Of course I take responsibility for those things that are put out under my name, but I was genuinely taken aback when this claim was brought to my attention and am both appalled and very sorry that an impression was given that was not accurate.”
Ms Roughley said she was “entirely responsible” for the website post and had offered her resignation.
“I am frankly mortified at the distress this issue has caused Paul and may have caused to anyone involved with the Hillsborough tragedy. I could not be more sorry.”
A Ukip spokesman said on Wednesday that the resignation had been rejected: “She has worked very long and hard for many, many years of loyal and effective service. We all make mistakes.
“Obviously Paul is grateful for her offer, but what sort of chap would he be to say her career is dead for what seems to be a minor error six years ago?”
Mr Nuttall’s statement made clear he stands by his account of being present at the disaster as a 12-year-old fan, after doubts were raised by The Guardian.
“From the upper tier of the Leppings Lane end of the Hillsborough Stadium, I watched the events of that day unfold with horror,” he said.