The Plymouth towers will have cladding removed after it emerged it was made of similar material to Grenfell Tower.
It was expected to be removed within days, but authorities now say it won't be taken down until at least November.
Plymouth Community Homes says additional safety precautions are in place to ensure its residents' safety.
More on tower block cladding delay and other Devon and Cornwall stories
Chloe Brewster, 22, fled her flat in the Mount Wise Tower estate with her baby after a fire broke out in one of the blocks earlier this year.
"It's absolutely horrifying to think that it's going to be at least to the end of the year that they're going to remove the cladding," she said.
"There is a highly likely chance of a fire happening between now and the end of the year.
"At the end of the day they're not the ones that are having nightmares about burning to death with a baby in a tower block."
Plymouth Community Homes said it would not follow Camden Council's decision to evacuate residents, because the Mount Wise towers have additional fires safety measures and precautions in place.
CEO John Clark said last week that the cladding would be removed "over the next couple of days".
But in a letter to residents on Tuesday the housing authority said specialist consultants had identified a target date for the removal of the panels by the end of November.
Labour MP Luke Pollard has also claimed that some people living in high-rise flats are being refused insurance renewals.

London Street in Norwich was pedestrianised on 17 July 1967.
The pedestrianisation of Norwich city centre is often referenced by fans of the fictional DJ, played by comedian Steve Coogan.
The Norwich Society said the city had "pioneered pedestrianisation in the UK".
Alan Partridge posed the question "what do you think about the pedestrianisation of Norwich city centre?" during an intimate scene.
In the episode from 1997, Partridge said: "I'll be honest, I'm dead against it. People forget that traders need access to Dixons.
"They do say it will help people in wheelchairs."
Norwich City Council approved plans to pedestrianise more parts of the city in 2015.
Paul Burall, vice chairman of the Norwich Society, said: "Norwich pioneered pedestrianisation in the UK and continues to extend the benefits, with another two streets being pedestrianised in the last two years.
"While a few local people agree with Alan Partridge and still want to be able to drive everywhere, the vast majority welcome the ability to walk around without the noise, pollution and potential danger from traffic, and the great majority of traders recognise the benefits as well."
Norwich is far from being the only town or city whose profile has been raised by its television connections.
During the pedestrianisation ceremony, the then Lord Mayor of Norwich CH Sutton tied - rather than cut - a ribbon across London Street to signify its closure to traffic.
Although other shopping areas - such as those in new towns like Stevenage - were made pedestrian-only long before London Street, the Norwich road was the first to be closed to motorised traffic and given over to pedestrians.
A young mother says she has nightmares about "burning to death" with her baby after work on three tower blocks was delayed.
[NEXT_CONCEPT]
A city whose traffic plans were made famous by Alan Partridge is marking 50 years since one of its roads became the first to be pedestrianised in England.