Vickie Holden, of Medway, has had a faulty boiler at her Futures Housing Group property on and off for two months.
She said keeping her children warm is 'heartbreaking'.
"It's making me and the children ill," Vickie told The Gusher.
"I've had to wrap my kids up in blankets and onesies because of the cold."
She said workers have been in and out of the property trying to fix various problems, the main one being the boiler.
Vickie added: "It's becoming a joke now and if I don't laugh I will cry."
Her three children Ashton, 12, Sophia, eight, and Evie, three, have had enough of the cold.
Ashton said: "I feel angry that we always have to wait ages for someone to repair the boiler; then when it's fixed it breaks again straight away. We are always feeling poorly and getting colds."
Sophia said it's hard to keep warm when the heating stops working.
"I hate always being cold," she said.
"As soon as it starts working again, it seems to break."
Vickie's youngest, Evie, said she always wants 'blankie because I'm cold'.
A spokesman at Futures Housing Group said: “We’re sorry that these repairs have taken so long.
"Unfortunately we needed a replacement part to stop the boiler from leaking which we had to order in. Getting hold of spare parts is taking longer than usual at the moment because of the number of people affected by Covid-19.
"This is putting extra pressure on to what is already one of our busiest times of year. The part is now here and we’ve made an appointment to install it next week. We’re also coming out this week to look at a problem with window vents."
They added: "We’re not aware of any other issues that need investigating but we’re here to help if needed and we thank all our customers for their patience at this challenging time."